seismic and rock-physics characterization of fractured ... · seismic and rock-physics...

$: SEISMIC AND ROCK-PHYSICS CHARACTERIZATION OF FRACTURED ... · seismic and rock-physics characterization of fractured reservoirs a dissertation submitted to the department of geophysics$
SEISMIC AND ROCK-PHYSICS

CHARACTERIZATION OF

FRACTURED RESERVOIRS

A DISSERTATION

SUBMITTED TO THE DEPARTMENT OF GEOPHYSICS

AND THE COMMITTEE ON GRADUATE STUDIES

OF STANFORD UNIVERSITY

IN PARTIAL FULFILLMENT OF THE REQUIREMENTS

FOR THE DEGREE OF

DOCTOR OF PHILOSOPHY

By

Li Teng

June, 1998

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© Copyright 1998

by

Li Teng

iii

I certify that I have read this dissertation and that in my

opinion it is fully adequate, in scope and quality, as a

dissertation for the degree of Doctor of Philosophy.

______________________________________

Gerald M. Mavko

(Principal Adviser)




______________________________________

Jerry M. Harris




______________________________________

Mark D. Zoback

Approved for the University Committee on Graduate Studies:

______________________________________

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ABSTRACT

Aligned fractures induce anisotropy into rock mechanical properties. Seismic

shear-wave splitting techniques have been used successfully to recover the symmetry-

plane orientation and the magnitude of the shear-wave anisotropy. This orientation

and magnitude correlate with the subsurface fractures' orientation and intensity.

Shear-wave data are not affected by the fluid properties. P-wave data are cheaper to

acquire, have a higher signal-to-noise ratio, contain pore-fluid information, and are

more available in 3D. However, the use of P-wave data in fracture detection and

characterization is not fully exploited.

I develop a methodology for using single-component 3D P-wave data in

characterizing naturally-occurring subsurface fractures, with the help of prior

knowledge acquired from geological observations, logs, and shear wave surveys.

This characterization includes determining the fracture orientation, density

distribution, aperture, and fracture-filling material under the in-situ temperature and

pressure conditions.

I combine the elastic properties of fractured rocks and the reflectivity formulas in

anisotropic media to derive the relationship between P-wave amplitude anisotropy

and fracture physical properties. Using Hudson's penny-shaped crack model, I show

that:

1) reflectivity anisotropy increases with crack density and fracture-filling fluid bulk

modulus, and decreases with crack aspect ratio;

2) under high-frequency conditions, it decreases with the background rock's Poisson's

ratio;

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3) the same fracture set induces more reflectivity anisotropy under high-frequency

conditions than under low-frequency conditions.

I demonstrate the first-order mathematical equivalence among three commonly

used fracture models, including Hudson's first-order penny-shaped-crack model,

Schoenberg-Muir's thin-layer model, and Pyrak-Nolte's frequency-dependent slip-

interface model. This equivalence shows that we can explain the observed seismic

anisotropy in terms of different fracture network configuration models. The

suitability of each fracture interpretation should be judged by the in situ fracture

observations.

The above results serve as a guide for fracture interpretation in field studies. I use

the seismic datasets from the Fort Fetterman site to explore and test the feasibility and

reliability of the using P-wave anisotropy in conjunction with S-wave data and other

available information to characterize the subsurface fracture network. The Fort-

Fetterman site is located at the southwestern margin of the Powder River Basin, in

Converse County, east-central Wyoming. The target reservoirs at the Niobrara and

the Frontier formations belong to the lower Cretaceous strata. The data available for

this study include well log data, multi-component VSP data, 2D shear wave data

(Line GRI-1 along north-south direction, and Line GRI-4 along east-west direction),

and 3D P-wave data. Geological observations of outcrops and FMS logs show that a

set N110oE+/-15o fractures appear in the Tertiary formations, and locally in the

Cretaceous formations; a set of N70oE+/-10o only occurs in the Cretaceous

formations, including the Niobrara and the Frontier formations. Dipole-sonic-log

analysis shows that the fracture orientation is along the N80oE+/-10o direction at the

reservoir level, and that the fractures tend to concentrate in low-porosity, high-clay-

content, thin layers rather than distributed evenly over large intervals. These results

are consistent with the outcrop observations. Shear-wave rotation analysis was

applied to both VSP and 2D-surface-shear-wave data. Whole-trace rotation shows a

direction of N96oE+/-10o for the VSP data, N105oE+/-10o for the 2D data along Line

GRI-4, N105oE+/-15o for the south part of Line GRI-1, and N75oE+/-15o for the north

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part of Line GRI-1. To recover the fracture information at the reservoir level, layer-

stripping analysis to remove the overburden effects is required. Layer-stripping

analysis is only successful in the CDP ranges along Line GRI-4 where the signal-to-

noise ratio is high. At those CDP locations, the shear-wave data give a fracture

orientations of N75oE+/-10o at the reservoir level. I derive the crack density from the

shear-wave data. The P-wave traveltime anisotropy predicts an apparent fracture

direction of N39oE+/-8o. This direction, however, is likely to be caused by the effect

of dip. In order to get meaniful fracture information from the P-wave traveltime data,

we need a fracture effect larger than the dip effect, or a higher signal-to-noise ratio.

P-wave amplitude analysis also gives a fracture orientation of N87oE+/-18o. The

magnitude of P-wave amplitude azimuthal variation is also higher than that predicted

by modeling. This is because the average crack density inferred from the P- and S-

wave traveltime data can be much less than the crack density in the thin fractured

layers inferred from the P-wave amplitude azimuthal variation at the boundary of the

thin fractured layers.

I investigate the type of subsurface fracture information that can be extracted

from seismic shear wave analysis, and show how rock physics and geostatistics can

be combined to give realistic interpretations. The synthetic results show that seismic

analysis can help to constrain predictions of the spatial distribution of fracture

densities, which, in turn, have a very important impact on fluid flow responses.

However, the inference of fracture densities from shear wave splitting analysis can be

unreliable due to uncertainties about some key parameters, including fracture specific

stiffness, fracture orientation, and background lithology variations. The uncertainty

in fracture orientation distribution does not affect significantly the final fracture

density estimates. The common assumption that anisotropy is induced by a single set

of parallel fractures can lead to misinterpretation of the fracture density field. In

addition, the length and orientation distributions of the fractures are crucial factors

determining connectivity of the fracture system and, therefore, have an important

impact on fluid recovery. The uncertainties can be reduced by considering additional

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information about the subsurface fracture system such as that coming from analog

outcrop data, geomechanical studies and production data. A reliable knowledge of

the lithology of the matrix rock is also important.

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ACKNOWLEDGMENTS

I feel very privileged to have studied at Stanford University for five and one-half

years. Now that my Ph.D. program has almost come to a close, I want to thank all the

faculty members, staff members, and students in the Geophysics Department who

have made my stay a rewarding and pleasant experience.

I sincerely thank my advisor, Professor Gary Mavko, for his inspiring advice,

countless hours of scientific discussions, teaching of invaluable presentation skills,

and continuous support. I am grateful to him and Professor Amos Nur, whose

continuous effort makes many research projects possible and fruitful at the Stanford

Rock Physics Group. I would like to express my gratitude to Professors Jim

Berryman, Kefeng Liu, Jerry Harris, and Mark Zoback for serving on my committee

and providing constructive suggestions.

I would like to thank Professor Francis Muir, Atilla Aydin, Jack Dvorkin, Biondo

Biondi, Tapan Mukerji , Dan Moos, Colleen Barton, and Wei Chen for many

insightful talks; Emmanual Gringarten for his help and contribution to the work

presented in this thesis; Ralf Schulz for letting me modify and use his reflectivity

program. I thank Margaret Muir and Linda Farwell for their great deal of help

during my study here. I thank Fannie Toldi for her help with editing my thesis. I

thank Madhumita Sengupta, Tapan Mukerji, Mario Gutierrez, Mickaele Ravelec, and

Christina Chan for once being my officemates, and always being my friends. I am

grateful to Dr. Barbara Mavko for her encouragement and friendship. My stay at

Stanford was made enjoyable by many other people: Manika Prasad, Ran Bachrach,

Rubina Sen, Yuguang Liu, Hui Wang, Per Avseth, Doron Galmudi, James Packwood

and many, many others. I thank them.

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My research was partly funded by the Gas Research Institute Contract 5094-210-

3235 and the Department of Energy. I am grateful for their financial support. The

scientists with Arco Exploration and Production, especially Keith Katahara, Robert

Withers, Dennis Corrigan, Gayle Laurin, and Tracey Skopinski, offered me a

tremendous amount of help in getting me the data and discussing the research. I

benefited from many discussions and a wonderful summer time working with Leon

Thomsen and Mike Mueller at Amoco World Wide Exploration and Production

Company. I also thank William Soroka, Wenjie Dong, and Paul Cunningham for the

fruitful summer with Mobil Technology Company. I thank Bertram Nolte, with

M.I.T., and Ilya Tsvankin, with Colorado School of Mines for sending me their

papers for references.

Last but not least, I thank my parents for their support and encouragement during

all the easy and tough time of my life.

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CONTENTS

1. Introduction . . . . . . . . . . . . . . . . . . . . . . 1

1.1 Research Motivation and Objectives . . . . . . . . . . . . . 1

1.2 Description of Chapters . . . . . . . . . . . . . . . . . 3

1.3 References . . . . . . . . . . . . . . . . . . . . . 5

2. Methodology of Fracture Network Characterization Using Seismic

Anisotropy . . . . . . . . . . . . . . . . . . . . . . 9

2.1 Introduction . . . . . . . . . . . . . . . . . . . . . 9

2.2 Three Elastic Theories of Fractured Rocks and Their Relationships . . . 11

2.3 Review of Fracture-Induced Anisotropy in P- and S-wave Velocities . . 19

2.4 Fracture-Induced Anisotropy in P-wave Reflectivity . . . . . . . . 24

2.5 The Characteristic Frequency of Local Fluid-Flow in Fractured Rocks . . 42

2.6 Using Probability Functions to Quantify the Uncertainty in Fracture

Characterization . . . . . . . . . . . . . . . . . . . 48

2.7 References . . . . . . . . . . . . . . . . . . . . . 56

3. Reservoir Rock Properties of Fort Fetterman Site . . . . . . . . . 60

3.1 Introduction . . . . . . . . . . . . . . . . . . . . . 60

3.2 Overview of Well Logs at the Survey Area . . . . . . . . . . 61

3.3 Spectral Gamma-Ray Logs and Clay Content . . . . . . . . . . 66

3.4 Pore Fluids . . . . . . . . . . . . . . . . . . . . . 70

3.5 Velocity and Density Analyses. . . . . . . . . . . . . . . 73

3.6 Evidence of Overpressure . . . . . . . . . . . . . . . . 80

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3.7 Indirect Evidences of Fractures. . . . . . . . . . . . . . . 80

3.8 FMS Logs and Fracture Number Count . . . . . . . . . . . . 83

3.9 Anisotropy in Dipole Sonic Logs . . . . . . . . . . . . . . 86

3.10 Conclusions . . . . . . . . . . . . . . . . . . . . 88

3.11 References . . . . . . . . . . . . . . . . . . . . . 89

4. Integrated Seismic Interpretation of Fracture Networks . . . . . . .

91

4.1 Introduction . . . . . . . . . . . . . . . . . . . . . 91

4.2 VSP shear-wave birefringence and 1D fracture-density distribution . . . 92

4.3 Surface shear-wave birefringence and 2D fracture-density mapping. . . 105

4.4 3D P-wave Velocity Anisotropy and 3D Fracture Network . . . . . 121

4.5 P-wave Amplitude Anisotropy and Fracture Properties . . . . . . . 134

4.6 Conclusions . . . . . . . . . . . . . . . . . . . . . 142

4.7 References . . . . . . . . . . . . . . . . . . . . . 145

5. Can Seismic Imaging help to quantify fluid flow in fractured rocks? . . . 146

5.1 Abstract . . . . . . . . . . . . . . . . . . . . . . 146

5.2 Introduction . . . . . . . . . . . . . . . . . . . . . 147

5.3 Procedures . . . . . . . . . . . . . . . . . . . . . 148

5.4 Uncertainty in Interpretation of Seismic Data for Fractures . . . . . 161

5.5 Discussion . . . . . . . . . . . . . . . . . . . . . 176

5.6 Acknowledgments. . . . . . . . . . . . . . . . . . . 179

5.7 References . . . . . . . . . . . . . . . . . . . . . 179

Appendix Reviews of the Geological Framework of the Study Site . . . . 182

A.1 Geological Settings of Fort Fetter Site and Powder River Basin . . . 182

A.2 Fracture Existence and Attributes . . . . . . . . . . . . . 190

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LIST OF TABLES

3.1 Five wells supplying digital well-log data . . . . . . . . . . . . 66

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LIST OF FIGURES

2.1 Reflection at the boundary between two fractured layers. . . . . . . . 31

2.2 (a) Gray scale contours and (b) 0°- and 90°-azimuth cross-sections of the

reflectivity at the top of a fractured rock calculated by the Zoeppritz equations

and the weak anisotropy approximation. . . . . . . . . . . . . 34

2.3 Reflectivity anisotropy versus crack density in a fractured rock at the interface

between an isotropic rock with Poisson's ratio 0.3 and the fractured rock with

Poisson's ratio 0.2. . . . . . . . . . . . . . . . . . . . 35

2.4 Reflectivity anisotropy versus crack aspect ratio at the interface between an

isotropic rock with Poisson's ratio 0.3 and a fractured rock with Poisson's ratio

0.2. . . . . . . . . . . . . . . . . . . . . . . . . 36

2.5 Reflectivity anisotropy versus Poisson's ratio of a fractured rock at the interface

between an isotropic rock with Poisson's ratio 0.3 and the fractured rock with

specified Poisson's ratio. . . . . . . . . . . . . . . . . . 37

2.6 P- versus S-wave velocity for the gas sands and brine sands collected by

Castagna and Smith (1994). . . . . . . . . . . . . . . . . 38

2.7 Classification of the gas sands based on the AVO behavior. . . . . . . 39

2.8 Reflectivity anisotropy vs Poisson's ratio at the shale/sandstone interfaces . 41

2.9 Diagram of local fluid flow in closely spaced cracks. . . . . . . . . 43

2.10 Diagram of local fluid flow in fractures with permeable walls. . . . . . 44

2.11 Permeability versus porosity for the three sets of rock samples. . . . . . 47

2.12 Normalized pressure (Pa) in a fracture with permeable walls versus wave

frequency. . . . . . . . . . . . . . . . . . . . . . . 47

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2.13 Characteristic frequency of local fluid flow in fractures with permeable walls

versus embedding-rock porosity. . . . . . . . . . . . . . . . 48

2.14 Laboratory measurement of bulk and shear moduli of 80 sandstone samples

measured by Han under various confining pressures. . . . . . . . . 51

2.15 Crack density as a function of traveltime anisotropy, calculated with the

deterministic approach. . . . . . . . . . . . . . . . . . . 51

2.16 Crack density probability as a function of observed traveltime anisotropy. . 54

2.17 Crack-density probability as a function of observed shear modulus. . . . 56

3.1 Base map of the Fort Fetterman site. . . . . . . . . . . . . . 62

3.2 Formation tops superimposed on the well logs from (a) the Red Mountain well,

(b) the State #1-36 well, (c) the Wallis well. . . . . . . . . . . . 63

3.3 (a) Well trajectories of the Red Mountain well showing both the vertical hole

(pilot hole) and the highly deviated hole (horizontal hole); (b) Map view of the

highly deviated hole showing that its azimuth is about N155oE.. . . . . 67

3.4 The spectral gamma ray logs recorded along the Red Mountain well. . . . 69

3.5 Statistical distribution of clay content of (a) the Niobrara Formation and (b) the

first Frontier Sand. . . . . . . . . . . . . . . . . . . . 69

3.6 (a) K-Th shale index (b) SP (c) the product of density and neutron porosity . 71

3.7 ILD logs expressed as resistivity along the Red Mountain well. . . . . 72

3.8 Range of the P-, S-wave velocities, density, and porosity based on the log

measurement of the Niobrara Formation along the Red Mountain well. . . 75

3.9 Crossplots of the P-wave velocity versus density, clay content, S-wave velocity,

and Vp-Vs ratio for the Niobrara Formation. . . . . . . . . . . . 76

3.10 Range of the P-, S-wave velocities, density, and porosity based on the log

measurement of the first Frontier Sand along the Red Mountain well. . . . 78

3.11 Crossplots of the P-wave velocity versus density, clay content, S-wave velocity,

and Vp-Vs ratio for the first Frontier Sand. . . . . . . . . . . . 79

3.12 The conductivity log and the density log along the Red Mountain well. . . 81

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3.13 Cross-plot of P-wave traveltime versus density of the Niobrara Formations

based on logs from the Red Mountain, the State #1-36, and the Wallis wells. 82

3.14 FMS display showing open fractures at the Frontier Formation level. . . . 84

3.15 The distributions of fracture strike and aperture based on the FMS logs. . . 85

3.16 Dipole sonic log (a) fast shear wave azimuth; (b) traveltime of the fast and slow

shear waves; (c) shear wave birefringence; (d) K-Th shale index, and (e) P-

wave sonic velocity. . . . . . . . . . . . . . . . . . . . 87

4.1 VSP survey map. . . . . . . . . . . . . . . . . . . . . 93

4.2 The 64 depth levels of the downhold geophone for the VSP survey. . . . 94

4.3 The four VSP S-wave components before the Alford rotation. . . . . . 95

4.4 The four VSP S-wave components after the Alford rotation of (a) 20o, (b) 30o,

(c) 40o, and (d) 60o. . . . . . . . . . . . . . . . . . . . 97

4.5 The four VSP S-wave components received at level #61 (depth 5000.3 ft) after

25o to 35o rotation. . . . . . . . . . . . . . . . . . . . 101

4.6 The time lag of between the fast and the slow VSP events. . . . . . . 104

4.7 The four components of shear wave along Line GRI-4. . . . . . . . 107

4.8 GRI-4 after 15o Alford rotation to N105oE direction. . . . . . . . . 108

4.9 Cross-correlation results for picking the traveltime lag. . . . . . . . 109

4.10 Shear-wave traveltime difference along Line GRI-4. . . . . . . . . 110

4.11 Shear-wave traveltime difference generated within each formation along Line

GRI-4. . . . . . . . . . . . . . . . . . . . . . . . 111

4.12 The shear-wave traveltime anisotropy in each formation along Line GRI-4. . 111

4.13 Results of layer stripping at the top of the Sussex sand, and the subsequent

Alford rotation to (a) N75Eo and (b) N110oE.. . . . . . . . . . . 113

4.14 The traveltime lag between the fast and slow events from the top of the Sussex

formation to the bottom of the first Frontier formation. . . . . . . . 114

4.15 The traveltime anisotropy in the Niobrara/Frontier formations. . . . . . 115

4.16 The crack density in the Niobrara and the first Frontier sand. . . . . . 116

4.17 The four components of shear wave along Line GRI-1. . . . . . . . 117

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4.18 GRI-1 after 15o Alford rotation to N105oE direction. . . . . . . . . 118

4.19 GRI-1 after -15o Alford rotation to N75oE direction. . . . . . . . . 119

4.20 Shear-wave traveltime difference along Line GRI-1. . . . . . . . . 120

4.21 The fracture directions predicted by the Alford-rotation analysis of the 2D

shear-wave data. . . . . . . . . . . . . . . . . . . . . 121

4.22 Partially stacked CDP superbin gathers along azimuth N45oE. . . . . . 124

4.23 P-wave 5000ft-to-8000ft far-offset stack of superbin at inline #135 and xline

#205. . . . . . . . . . . . . . . . . . . . . . . . . 125

4.24 Cross-correlation results of P-wave traces along 5 o and 95 o azimuths. . . 126

4.25 P-wave traveltime between the top of Sussex and the bottom of the first Frontier

Sand along various azimuths. . . . . . . . . . . . . . . . . 127

4.26 Histogram of the fast P-wave direction, i.e., the fracture orientation, predicted at

the superbin at inline #135 and xline #205. . . . . . . . . . . . 129

4.27 Histogram of the P-wave traveltime azimuthal variation from the top of Sussex

to the bottom of the first Frontier Sand at the superbin at inline #135 and xline

#205. . . . . . . . . . . . . . . . . . . . . . . . . 130

4.28 Mean value and standard deviation of the predicted fast Vp direction based on

P-wave traveltime anisotropy. . . . . . . . . . . . . . . . . 131

4.29 The diagram of P-wave reflected at a dipping bed . . . . . . . . . 132

4.30 Dip-induced apparent traveltime anisotropy as a function of the dip angle of the

reflector. . . . . . . . . . . . . . . . . . . . . . . . 132

4.31 Fracture orientations predicted by P-wave traveltime anisotropy overlapped by

the isopach map. . . . . . . . . . . . . . . . . . . . . 133

4.32 Predicted Vp anisotropy for the Niobrara and Frontier formations, containing

parallel fractures with crack density 0.012, aspect ratio from 0.0001 to 0.1, and

various types of crack-filling fluid. . . . . . . . . . . . . . . 134

4.33 The amplitude variation with azimuth at the superbin at inline #135 and xline

#205. . . . . . . . . . . . . . . . . . . . . . . . . 136

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4.34 Histogram of the observed fracture orientations based on the P-wave amplitude

variation with azimuth. . . . . . . . . . . . . . . . . . . 136

4.35 Histogram of the estimated azimuthal variation in P-wave amplitude shown in

percentage. . . . . . . . . . . . . . . . . . . . . . . 137

4.36 The blocked log data used in the modeling as the properties of the unfractured

rocks. . . . . . . . . . . . . . . . . . . . . . . . . 138

4.37 The reflectivity at the bottom of the fractured first Frontier Sand that contains

parallel vertical fractures with a crack density 0.1. . . . . . . . . . 138

4.38 The reflectivity azimuthal anisotropy at the bottom of the fractured first Frontier

Sand that contains parallel vertical fractures with a crack density 0.012. . . 139

4.39 The reflectivity azimuthal anisotropy at the bottom of the fractured first Frontier

Sand that contains parallel vertical fractures with a crack density 0.1. . . . 140

4.40 The crack orientations derived from the 3D P-wave amplitude azimuthal

variation. . . . . . . . . . . . . . . . . . . . . . . 141

4.41 The crack orientations derived from the 3D P-wave amplitude azimuthal

variation. Only fracture orientations that have a standard deviation of less than

20o are plotted.. . . . . . . . . . . . . . . . . . . . . 142

5.1 Reference fracture image digitized from a photo of an exposed outcrop . . 149

5.2 (a) Diagram of a set of parallel fractures in Cartesian coordinates; (b) diagram

of a set of fractures uniformly distributed within a angle range in Cartesian

coordinates; (c) diagram of two sets of vertical fractures in Cartesian

coordinates. . . . . . . . . . . . . . . . . . . . . . 150

5.3 Fracture density maps of the reference fracture image for (a) Set I and (b) Set II;

azimuth spread maps (degrees) for (c) Set I and (d) Set II in each block

consisting of 68 by 52 pixels (17m by 13m). . . . . . . . . . . . 153

5.4 Forward modeling results of (a) shear wave moduli (GPa) and (c) velocities

(km/s) for vertical propagating shear wave polarized along the E-W direction,

(b) shear wave moduli and (d) velocities for shear waves polarized along the N-

S direction, (e) shear wave anisotropic parameter. . . . . . . . . . 154

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5.5 Fracture density estimation for Case 1 (parallel fracture assumption): (a) integer

part for Set I; (b) integer part for Set II; (c) residual decimal part for Set I; (d)

residual decimal part for Set II. . . . . . . . . . . . . . . . 156

5.6 Four equiprobable realizations of the fracture system for Case 1 assuming

parallel fractures for both sets. . . . . . . . . . . . . . . . 157

5.7 Tracer saturation profile after breakthrough through the fractured formation

containing the reference fracture network. . . . . . . . . . . . . 159

5.8 Recovery and tracer-cut responses for 50 equiprobable simulations (gray lines)

along with the responses of the reference image (black line). . . . . . 160

5.9 Fracture density maps for Case 2 for (a) Set I and (b) Set II assuming that the

fracture shear specific stiffness is 50 MPa/mm; (c) simulated fracture network

based on the density maps in (a) and (b). . . . . . . . . . . . . 162

5.10 Recovery and tracer-cut responses for Case 1 and Case 2. . . . . . . 162

5.11 Fracture density maps for Case 3 for (a) Set I and (b) Set II by taking the true

fracture angle distribution into account; (c) simulated fracture network based on

the density maps in (a) and (b) and the true fracture angle distribution. . . 164

5.12 Fracture density maps for Case 4 and 5 assuming 20° angle distribution for (a)

integer part of Set I; (b) integer part of Set II; (c) decimal part of Set I; (d)

decimal part of Set II. . . . . . . . . . . . . . . . . . . 165

5.13 Simulated fracture networks for (a) Case 4 and (b) Case 5. . . . . . . 166

5.14 Recovery and tracer-cut responses for Cases 3, 4, and 5. . . . . . . . 166

5.15 Fracture density maps for Case 6 for (a) Set I and (b) Set II; (c) simulated

fracture network based on the density maps in (a) and (b). . . . . . . 168

5.16 Recovery and tracer-cut responses for Case 6. . . . . . . . . . . 168

5.17 Lab measurement of P- and S-wave velocities of tight gas sandstone samples

under 40 MPa effective pressure. The data are from Jizba (1991). . . . . 170

5.18 Velocity map (km/s) of the background unfractured rock for Case 7. The

velocity spatial variation in the E-W direction is about 20% with a small

random variation along the N-S direction. . . . . . . . . . . . . 170

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5.19 The shear wave moduli (GPa) and velocities (km/s) of the fractured formation

for Case 7. (a) shear modulus for E-W polarization; (b) shear modulus for N-W

polarization; (c ) shear wave velocity for E-W polarization; (d) shear wave

velocity for N-S polarization. . . . . . . . . . . . . . . . . 171

5.20 Density maps for Case 7 for (a) Set I and (b) Set II, (c) simulated fracture

network based on the density maps in (a) and (b). . . . . . . . . . 172

5.21 Recovery and tracer-cut responses for Case 7. . . . . . . . . . . 172

5.22 Simulated fracture networks: (a) Case 8 - maximum fracture length is 7.5 m (30

pixels); (b) Case 9 - maximum fracture length is 22.5 m (90 pixels).; (c ) Case

10 - maximum fracture length is 45 m (180 pixels).. . . . . . . . . 174

5.23 Recovery and tracer-cut responses for Cases 8, 9, and 10. . . . . . . 174

5.24 Simulated fracture networks: (a) Case 11 - no length constraint, parallel

fractures; (b) Case 12 - maximum fracture length is 7.5 m; azimuth spread is

20°; (c) Case 13 - maximum fracture length is 22.5 m; azimuth spread is 20°;

(d) Case 14 - maximum fracture length is 45 m; azimuth spread is 20°. . . 176

5.25 Recovery and tracer-cut responses for Cases 11, 12, 13, and 14. . . . . 177

1

CHAPTER 1

INTRODUCTION

1.1 Research Motivation and Objectives

Because fractures largely control in-situ permeability and rock strength, fracture

detection is very important in hydrocarbon recovery, mine stability, waste isolation,

and earthquake studies.

In the oil and gas industry, the emphasis is shifting from basic exploration to

improved recovery rates of existing fields. When there are fracture-controlled

reservoirs, understanding the subsurface fracture networks is important to optimize

well planning and production. A large portion of oil and natural gas in the world is

trapped in tight reservoirs (Nelson, 1985). In such formations, often the only

practical means of extracting the gas/oil is to use the increased drainage surface

provided by natural fractures, which controls fluid storage and mobility. The reverse

effect is that fractures can provide the paths for the injected steam or water to bypass

the matrix pores, and cause the slow-down or termination of hydrocarbon production

(Massonnat, 1994). In both situations, locating the subsurface fractured zones and

obtaining the fractures' physical properties, such as fracture orientation and aperture,

will help to optimize the field development plan.

Although many logging tools and log-analysis methods, such as the borehole

televiewer and formation MicroScanner (Schlumberger, 1989), have been designed to

view the subsurface fractures cutting through a borehole, their usage is limited by the

Chapter 1 - Introduction 2

high cost and small sampling area. The information obtained is very valuable direct

information about the subsurface fractures' geometry, fluid content, spacing, and

connectivity. However, the interpolation of fracture-network properties over a field is

inevitably inaccurate when there are only a few wells with fracture information.

A seismic survey has the advantages of low cost, wide coverage, and deep

penetration. Theoretical and laboratory studies (Nur, 1971; Crampin and Bamford,

1977; Hudson, 1980, 1981, 1990, 1994; Yin, 1992) have shown that fractures can

induce anisotropy into seismic properties of the rocks. The seismic survey has the

potential to be a powerful tool to detect and characterize subsurface fractures. The

mainstream in seismic fracture detection uses the shear-wave splitting techniques first

suggested by Alford (1986). These techniques have been used successfully in

locating the fractured zones in many field studies (Queen and Rizer, 1990; Liu,

Crampin, and Queen, 1991; Mueller, 1991, 1992, 1994; Lewis et al., 1991;

Winterstein and Meadows, 1991a, b).

P-wave data are cheaper to acquire, have a higher signal-to-noise ratio, and are

more commonly available in 3D than shear-wave data. However, the use of P-wave

data in fracture detection and characterization is not fully exploited. There have been

both theoretical work and field observations showing the correlation between the

fractured zones and the azimuthal variation in P-wave amplitude and velocity

(Crampin and Bamford., 1977; Lefeuvre, 1993; Lynn et al., 1996; Ramos and Davis,

1997; Rueger 1996). The outputs of these studies were often the anisotropy mapped

over the survey areas. Some authors converted the amount of anisotropy to crack

density, according to the penny-shaped crack model (Hudson, 1980, 1981, 1990,

1994). However, they did not take into account realistic in-situ physical conditions,

including subsurface temperature, pressure, nature of fracture-filling material, seismic

frequency, and the hydraulic interaction between fractures. Critical problems remain

in estimating the subsurface fracture properties under in-situ reservoir conditions.

Gaps also exist in integrating all the information measured at core, log, and seismic

(including P- and S-wave surveys) scales for fracture characterization.


The objective of this thesis is to develop methodologies for characterizing

naturally-occurring subsurface fractures, with emphasis on using single-component

3D P-wave data with the help of prior knowledge acquired from logs and shear wave

surveys. This characterization includes determining the fracture orientation, density

distribution, aperture, fracture-filling material, and fracture hydraulic connectivity

under the in-situ temperature and pressure conditions. The significance of the

fracture-distribution mapping over the 3D-survey area is the potential for constraining

the underlying permeability distribution, which is critical for field planning and

development.

1.2 Description of Chapters

The chapters in this thesis present the theories and applications by which

subsurface fractures can be characterized by the use of P-wave data, with the help of

the rock and fracture information acquired from well logs and shear-wave seismic

surveys.

Chapter 2 describes the methodology of fracture-network characterization using

seismic anisotropy. I first discuss various elasticity theories of fractured media; these

theories link the physical properties of fractures to seismic anisotropy. These theories

include the first-order penny-shaped crack model (Hudson, 1981, 1990; Thomsen,

1995), the thin-layer model (Schoenberg and Muir, 1989), and the frequency-

dependent slip-interface model (Pyrak-Nolte et al., 1990a, b). I found that these

models are mathematically equivalent descriptions of fractured media. The same

amount of anisotropy in a fractured rock can be caused by either penny-shaped cracks

or large fractures cutting through the rock. To use the acquired seismic data to

characterize the in-situ fractures, we need prior knowledge of the fracture shape, so

we can choose the appropriate model.

I then review the fracture-induced traveltime/velocity anisotropy in both P- and S-

wave data, and derive the equations for P-wave reflectivity at the boundaries of


fractured rocks. When parallel vertical fractures are the sources for anisotropy, the

traveltime and the P-wave reflectivity vary with azimuth. I explore the effects of

fracture intensity, aperture, fracture-filling fluids, subsurface temperature, pressure,

fracture hydraulic connectivity, and seismic frequency, on the velocity and amplitude

azimuthal variations.

The seismic response over fractured formations is frequency-dependent (Biot,

1956; Mavko and Nur, 1979). I analyzed the characteristic frequency of local fluid

flow between fractures and the surrounding matrix through the fractures' permeable

walls.

In the last section of Chapter 2, I provide an example of using a probability

method to quantify the uncertainty in the fracture density estimation based on shear

wave splitting data. This is an anisotropic extension of the probability method

proposed by Mavko and Mukerji (1995) to quantify the uncertainty in hydrocarbon

indicators.

With this theoretical framework, I proceed to apply and test the methodology on

field data. I have access to data from well logs, a 4-component shear-wave VSP

survey, two 2D lines of a 9-component surface seismic survey, and a 3D P-wave

survey collected over a tight gas reservoir at the Fort Fetterman site, in the Powder

River Basin, east-central Wyoming. The data were made available by the funding

from the Gas Research Institute, Department of Energy, ARCO, and AMOCO.

Chapter 3 analyzes the well-log data at the Fort Fetterman site, and gathers the

typical rock property data at the reservoir level. These properties include the P- and

S-wave velocities, densities, clay content, pore fluids, evidence of overpressure, and

fracture indicators. The main goal is to assist fracture interpretation by the use of the

seismic anisotropy described in Chapter 4. Understanding the basic rock properties is

also an integral part of understanding the fractured reservoirs.

Chapter 4 analyzes the velocity anisotropy in the VSP and 2D surface shear-wave

data, and the azimuthal variation in the 3-D P-wave velocity and amplitude. I give

an integrated interpretation of the subsurface fracture system at the reservoir level.


This interpretation is based on the seismic anisotropy as well as the results of the

well-log analysis.

Chapter 5 presents the collaborative work with Emmanuel Gringarten, Gary

Mavko, and André Journel. We investigate the types of subsurface fracture

information that can be extracted from seismic shear-wave analysis; show how rock

physics and geostatistics can be combined to give realistic interpretations; illustrate

the variability (non-uniqueness) in the interpretations by showing equally probable

fracture predictions; and evaluate the uncertainty in rock physics interpretations by

looking at the results of some simple fluid-flow simulation.

In the appendix, I give readers an overview of the structural features, regional

stratigraphy, and fracture observations at the study site. It contains a summary of the

report, "Regional Geological Framework and Site Description" (Walters, Chen, and

Mavko, 1994). I also review observations of fracture existence and attributes in the

southern Powder River Basin (May et al., 1996), and at Moxa Arch and the adjacent

Green River Basin in southwestern Wyoming (Laubach, 1991, 1992a, 1992b; Dutton

et al., 1992).

1.3 References

Alford, R. M., 1986, Shear data in the presence of azimuthal anisotropy: Dilley,

Texas, SEG 56th Annual Meeting Expanded Abstracts.

Biot, M.A., 1956, Theory of propagation of elastic waves in a fluid saturated porous

solid. I. Low frequency range and II. Higher-frequency range, J. Acoust. Soc.

Amer., 28, 168-191.

Crampin, S., and Bamford, D., 1977, Inversion of P-wave velocity anisotropy,

Geophys. J R. astr. Soc., 49, 123.

Dutton, S.P., Hamlin, H. S., and Laubach, S. E., 1992, Geologic controls on reservoir

properties of low-permeability sandstone, Frontier Formation, Moxa Arch,

southwest Wyoming: The University of Texas at Austin, Bureau of Economic


Geology, topical report no. GRI-92/0127, prepared for the Gas Research Institute,

199 p.

Hudson, J. A., 1980, Overall properties of a cracked solid, Math. Proc. Camb. Phil.

Soc., 88, 371-384.

Hudson, J. A., 1981, Wave speeds and attenuation of elastic waves in material

containing cracks: Geophys. J. Roy. Astr. Soc., 64, 133-150.

Hudson, J. A., 1990, Overall elastic properties of isotropic materials with arbitrary

distribution of circular cracks, Geophys. J. Int., 102, 465-469.

Hudson, J. A., 1994, Overall properties of anisotropic materials containing cracks,

Geophys. J. Int., 116, 279-282.

Laubach, S.E., 1991, Fracture patterns in low-permeability-sandstone gas reservoir

rocks in the Rocky Mountain region, SPE Paper 231853, Proceedings, Joint SPE

Rocky Mountain regional meeting/low-permeability reservoir symposium, 501-

510.

Laubach, S.E., 1992a, Identifying key reservoir elements in low-permeability

sandstones: natural fractures in the Frontier Formation, southwestern Wyoming,

In Focus-Tight Gas Sands, GRI, Chicago, IL, 8, No. 2, 3-11.

Laubach, S.E., 1992b, Fracture networks in selected Cretaceous sandstones of the

Green River and San Juan basins, Wyoming, New Mexico, and Colorado, in

Geological Studies Relevant to Horizontal Drilling in Western North America, ed.

Schmoker, J.W., Coalson, E.B., Brown, C.A., 115-127.

Lefeuvre, Frederic, 1993, Fracture related anisotropy detection and analysis; and if

the P-waves were enough?, SEG Expanded Abstracts, 64, 942-945.

Lewis, C., Davis, T.L., and Vuillermoz, C., 1991, Three-dimensional multicomponent

imaging of reservoir heterogeneity, Silo Field, Wyoming, Geophysics, 56, 2048-

2056.

Liu, E., Crampin, S., and Queen, J., 1991, Fracture detection using crosshole surveys

and reverse vertical seismic profiles at the Conoco Borehole Test Facility,

Oklahoma, Geophys. J. Int., 107, 449-463.


Lynn, H., Simon, K. M., Bates, R., and Van Dok, R., Azimuthal anisotropy in P-wave

3-D (multiazimuth) data, 1996, Leading Edge, 15, No. 8, 923-928.

Massonnat, G. J., Umbhauer, F., and Odonne, F., 1994, The use of 3-D seismic in the

understanding and monitoring of waterflooding in a naturally fractured gas

reservoir, AAPG Bulletin, 78, no. 7, 1155.

Mavko, G., and Mukerji, T., 1995, A rock physics strategy for quantifying

uncertainty in common hydrocarbon indicators, American Geophysical Union

1995 fall meeting Eos Transactions, 76, No. 46, 600.

Mavko, G., and Nur, A., 1979, Wave attenuation in partially saturated rocks,

Geophysics, 44, No. 2, 161-178.

May, J., Mount, V., Krantz, B., Parks, S., and Gale, M., 1996, Structural framework

of southern Powder River Basin: a geologic context for deep, northeast-trending

basement fractures, ARCO-GRI fractured reservoir project report.

Mueller, M. C., 1991, Prediction of lateral variability in fracture intensity using

multicomponent shear-wave surface seismic as a precursor to horizontal drilling

in the Austin Chalk, Geophys. J. Int., 107, 409-415.

Mueller, M. C., 1992, Using shear waves to predict lateral variability in vertical

fracture intensity, Geophysics: The Leading Edge of Exploration, 11, No. 2, 29.

Mueller, M.C., 1994, case studies of the dipole shear anisotropy log, SEG Expanded

Abstract, 64, 1143-1146.

Nelson, R. A., 1985, Geologic Analysis of Naturally Fractured Reservoirs, Houston :

Gulf Pub. Co., Book Division, c1985.

Nur, A., 1971, Effects of stress on velocity anisotropy in rocks with cracks, J.

Geophys. Res., 76, 2022-2034.

Pyrak-Nolte, L. J., Myer, L. R., Cook, N. G. W., 1990a, Transmission of seismic

waves across single natural fractures, J. Geophys. Res., 95, No. B6, 8617-8638.

Pyrak-Nolte, L. J., Myer, L. R., Cook, N. G. W., 1990b, Anisotropy in seismic

velocities and amplitudes from multiple parallel fractures, J. Geophys. Res., 95

No. B7, 11345-11358.


Queen, J.H., Rizer, W.D., 1990, An integrated study of seismic anisotropy and the

natural fracture system at the Conoco borehole test facility, Kay county,

Oklahoma, J. Geophys. Res., 95, 11255-11273

Ramos, A.C.B., Davis, T., 1997, 3-D AVO analysis and modeling applied to fracture

detection in coalbed methane reservoirs, Geophysics, 62, 1683-1695

Rueger, A., 1996, Variation of P-wave reflectivity with offset and azimuth in

anisotropic media, SEG Annual Meeting Abstracts, 66, 1810-1813.

Schlumberger, 1989, Log interpretation principles/applications, Schlumberger

Educational Services.

Schoenberg, M and Muir, F, 1989, A calculus for finely layered anisotropic media,

Geophysics, 54, 581-589.

Thomsen, L., 1995, Elastic anisotropy due to aligned cracks in porous rock,

Geophysical Prospecting, 43, No. 6, 805-829.

Walters, R., Chen, W., Mavko, G., 1994, Regional geological framework and site

description, DOE report.

Winterstein, D.F., Meadows, M.A., 1991a, Shear-wave polarizations and subsurface

stress directions at Lost Hills field, Geophysics, 56, 1331-1348.

Winterstein, D.F., Meadows, M.A., 1991b, Changes in shear-wave polarization

azimuth with depth in Cymric and Railroad Gap oil fields, Geophysics, 56, 1349-

1364.

Yin, H., 1992, Acoustic velocity and attenuation of rocks: isotropy, intrinsic

anisotropy, and stress-induced anisotropy, Ph.D. dissertation, Stanford University,

Stanford, California.

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To detect and characterize fractures from seismic or sonic log data, we need to

use elasticity theories that link the mechanical properties of fractured rocks to the

fractures’ physical properties. Each of the three well-known models, Hudson’s penny-

shaped-crack model, Schoenberg and Muir’s slip-interface model, and Pyrak-Nolte’s

frequency-dependent slip-interface model, gives a different elasticity formulation. I

demonstrate that the first two models and the low-frequency limit of Pyrak-Nolte’s

model are mathematically equivalent to first order. The significance of this

equivalence is that different types of fracture configuration can give the same seismic

anisotropy pattern. Using seismic data cannot distinguish anisotropy induced by

penny-shaped cracks from that induced by long parallel-wall fractures. The

suitability of each model’s use in seismic fracture interpretation can be judged only by

in-situ fracture observations.

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Fracture detection and characterization is of great importance to hydrocarbon

recovery and waste isolation because fractures greatly impact the rocks’ overall

permeability and fluid flow (Nelson 1985). In order to characterize the physical

properties of fractures from the measurements of rock mechanical properties,

including seismic velocity, we need to use the elasticity theories of fractured rocks (I


call them fracture models for simplicity) that link the fractures’ physical descriptions

to rock elasticity.

There are three widely used fracture models: Hudson’s (1980, 1981, 1990, 1994)

penny-shaped-crack model, Schoenberg and Muir’s (1983, 1988, 1989) thin-layer

model, and Pyrak-Nolte’s (1990a, b) slip-interface model. They have different

assumptions, and are suitable for different fracture configurations. Hudson’s and

Schoenberg and Muir’s models are the long-wavelength-limit effective medium

theories. In contrast, Pyrak-Nolte’s model is not derived for long wavelength limit. It

takes fracture inertial effect into account and gives frequency-dependent seismic

wave velocities. I show how these models are mathematically equivalent to each

other to the first order. Their equivalence reveals that penny-shaped cracks and an

equivalent amount of parallel-wall long fractures can generate the same seismic

anisotropic response. The only way to distinguish between them is to rely on in-situ

fracture observations in cores and outcrops.

��5HODWLRQVKLS�%HWZHHQ�+XGVRQV�DQG�6FKRHQEHUJ�DQG�0XLUV�0RGHOV

I first review the two effective medium theories given by Hudson (1980, 1981,

1990, 1994), and Schoenberg and Muir (1983, 1988, 1989), and then show their

equivalence.

Hudson’s model is an intuitive, effective-medium theory that assumes an elastic

solid with an internal distribution of thin penny-shaped ellipsoidal cracks. Hudson

used crack density ( H ) and aspect ratio (a ) to describe the structure of fracture

systems. The crack density H is defined as:

paf

�� == D

91

H , (2.1)


where a is crack radius, N/V is the number of cracks per unit volume, f is crack-

induced porosity, and a is aspect ratio. The effective moduli are given as

��

LMLMLM

HII

LM &&&& ++= , (2.2)

where �

LM& ’s are the isotropic background moduli and �

LM& ’s, �

LM& ’s are the first- and

second-order corrections, respectively, that depend on the crack orientation, density,

and aspect ratio. We can calculate crack-induced porosity based on Equation 2.1 and

apply fluid substitution relationships in this model. Moreover, this theory is well

developed for diverse crack distributions, including one or more sets of parallel

fractures, conical distribution, and random distribution. The major limitation is that it

works only for small crack density ( H < 0.1) and small aspect ratio. For a single

crack set with crack normals aligned along the 3-axis, the cracked medium shows

transversely isotropic symmetry, and the first order corrections are

�

�

�

��H8&

ml

-=(2.3a)

�

�

��

��H8&

mmll +

-= (2.3b)

�

�

�

��

��H8&

mml +

-=(2.3c)

�

�

��H8& m-= (2.3d)

��

��=& (2.3e)

where l and m are the Lamé constants of the unfractured rock, U1, U3 depend on

crack conditions. For dry cracks, U1, U3 are


��

� mlml

++

=8(2.4a)

��

� mlml

++

=8 (2.4b)

For "weak" inclusions, when ( )[ ]�� mma +. is of the order of 1 and is not small

enough to be neglected (Mavko, Mukerji, and Dvorkin, 1998), Equations 2.4a and b

become

08

+++

=��

��

� mlml

(2.5a)

kmlml

+++

=��

��

�8 (2.5b)

where

( )( )mlpam

mlm��

++

=0(2.5c)

( )[ ]( )( )mlpam

mlmk

+++

=��.

(2.5d)

with K’ and m ’ the bulk and shear modulus of the inclusion material.

6FKRHQEHUJ� DQG� 0XLUV� VOLS�LQWHUIDFH� PRGHO� LV� EDVHG� RQ� WKH� %DFNXV� DYHUDJH

��DQG�UHSUHVHQWV�IUDFWXUHV�E\�LQILQLWHO\�WKLQ�OD\HUV��7KLV�PRGHO�ZRUNV�IRU�RQH�RU

PRUH� VHWV� RI� SDUDOOHO� IUDFWXUHV�� DQG� LW� GRHV� QRW� KDYH� WKH� ORZ�GHQVLW\� OLPLWDWLRQ�

+RZHYHU��EHFDXVH�LW�XVHV�DQ�LQILQLWHO\�WKLQ�FRPSOLDQW�OD\HU�GHVFULSWLRQ�WKDW�GRHV�QRW

FRQWDLQ�SRURVLW\�LQIRUPDWLRQ��ZH�FDQQRW�DSSO\�IOXLG�VXEVWLWXWLRQ�KHUH��)RU�RQH�VHW�RI

SDUDOOHO� IUDFWXUHV� ZLWK� QRUPDOV� DOLJQHG� DORQJ� WKH� ��D[LV�� WKH� HIIHFWLYH� FRPSOLDQFH

PDWUL[�LV


Sijeff = Sij

0 + DSij (2.6)

ZKHUH�Sij0 ��LV�WKH�LVRWURSLF�EDFNJURXQG�FRPSOLDQFH��DQG

ßßßßßßßß

à

Þ

ÏÏÏÏÏÏÏÏ

Ð

Î

=D

��

��

��

��

��

��

7

7

1

ILM

6

6

6K6 (2.7)

ZLWK� 16 ��DQG� 7

6 �WKH�QRUPDO�DQG�VKHDU�FRPSOLDQFH�RI�GLPHQVLRQ�OHQJWK�VWUHVV��7KH\

DUH�GHILQHG�DV�WKH�IUDFWXUH�GLVSODFHPHQW�SHU�XQLW�VWUHVV�DSSOLHG�� hf ��LV� WKH�YROXPH

IUDFWLRQ� RI� WKH� IUDFWXUHV�� L�H�� WKH� UDWLR� RI� IUDFWXUH� WKLFNQHVV� WR� IUDFWXUH� VSDFLQJ�

6FKRHQEHUJ��DOVR�JDYH�WKH�HIIHFWLYH�VWLIIQHVV�H[SUHVVLRQV�

��@��> &(&

1g--= (2.8a)

�� && g-= (2.8b)

1(

&+

=g

m��

(2.8c)

7(

&+

=��

m(2.8d)

C66 = m (2.8e)

where

EN =m

Hk N

=N

L

mk N

(2.9a)


ET =m

Hk T

=N

L

mkT

(2.9b)

mlm

g��

�

+==

3

6

9

9(2.9c)

+HUH�� m �LV�WKH�VKHDU�PRGXOXV�RI�WKH�XQIUDFWXUHG�URFN��kN �DQG�k T �DUH�WKH�QRUPDO�DQG

VKHDU�VSHFLILF�VWLIIQHVV�RI�WKH�IUDFWXUHV��+�LV�WKH�IUDFWXUH�VSDFLQJ��/�LV�WKH�OHQJWK�RI�D

URFN�VDPSOH��DQG�1�LV�WKH�QXPEHU�RI�IUDFWXUHV�LQVLGH�WKH�URFN�VDPSOH�

Using the relationship between stiffness matrix and compliance matrix,

( ) �aa -

= 6& (2.10)

we transform Equation 2.7 to stiffness domain, by

( )( )( )( ) �

��

��

�

��

�

aaa

aaa

aa

aaa

&6&

&66

&6

&&&

HII

HII

-D+=

-D+=

-=

-=D

-

-

-

-

(2.11)

7KH�DQDO\WLFDO�UHVXOWV�RI�(TXDWLRQ��DUH

( ) 1I

1I

6K

6K&

ml

l

��

�

�� ++-=D (2.12a)

( )( ) 1I

1I

6K

6K&

ml

mll

��

�� ++

+-=D (2.12b)

( )( ) 1I

1I

6K

6K&

ml

ml

��

� �

�� ++

+-=D (2.12c)


7I

7I

6K

6K&

m

m

+-=D�

�

�� (2.12d)

DC66 = 0 (2.12e)

&RPSDULQJ�(TXDWLRQ��ZLWK�(TXDWLRQV��DQG��ZH�JHW

( ) H8H8

6K+ 1I

1 �

�

��

mlmk +-== (2.13a)

H8H8

6K+ 7I

7 �

��

mmk -== (2.13b)

The above formulae demonstrate that the elastic anisotropy describe by the first-

order Hudson’s model is equivalent to that of Schoenberg and Muir’s slip-interface

model even though the fracture description is very different. Nichols (1990) used

group theory approaches and derived similar results. With these relationships, we can

derive the porosity information from Schoenberg and Muir’s parameters: we

transform the spacing and specific stiffness of fractures to crack density and aspect

ratio, and then use fluid substitution. Equations 2.13a and 2.13b also explain

Hudson’s small-crack-density limitation: large crack density can give negative

denominators in Equations 2.13a and 2.13b, and yield unrealistic negative fracture

stiffness.

��5HODWLRQVKLS�EHWZHHQ�3\UDN�1ROWHV�0RGHO�DQG�7ZR�(IIHFWLYH�0HGLXP

7KHRULHV

3\UDN�1ROWH�FKDUDFWHUL]HG�IUDFWXUHV�E\�IUDFWXUH�VSDFLQJ�DQG�VSHFLILF�VWLIIQHVV�� DV

LQ� 6FKRHQEHUJ� DQG� 0XLUV� PRGHO�� %XW� VKH� WRRN� WKH� IUDFWXUH� LQHUWLDO� HIIHFW� LQWR

DFFRXQW��6KH�FRQVLGHUHG�HDFK�IUDFWXUH�DV�D�VFDWWHULQJ�ERXQGDU\��7KLV�PRGHO�JLYHV�D


IUHTXHQF\�GHSHQGHQW� JURXS� YHORFLW\�� 7KH� 3�ZDYH� JURXS� YHORFLW\� SURSDJDWLQJ

SHUSHQGLFXODU�WR�WKH�IUDFWXUH�SODQH�LV

( )[ ]{ }( )[ ] ( )11

1HII

/18==

=88

kkwkw

��

��

�

+++

= (2.14)

with k N the normal specific stiffness of fractures, w the wave frequency, and = the

seismic impedance of the isotropic background rock:

Z = rU (2.15)

In order to find the connection between Pyrak-Nolte’s and Schoenberg and Muir’s

models, we compare the group velocity derived from the two theories. For Pyrak-

Nolte’s low-frequency long-wavelength limit ( ��w ), Equation 2.14 reduces to

Ueff =U

1 + NUZ / 2LkN( )(2.16)

The first-order approximation is

( )[ ] ßà

ÞÏÐ

Î +-=-

1

1HII +8/18=88

kml

k�

�� (2.17)

2Q�WKH�RWKHU�KDQG��EHFDXVH�WKH�SKDVH�YHORFLW\�DQG�WKH�JURXS�YHORFLW\�DUH�WKH�VDPH�IRU

ZDYHV�SURSDJDWLQJ�DORQJ� WKH�V\PPHWU\�D[LV�RI�D� WUDQVYHUVHO\� LVRWURSLF�PHGLXP��ZH

FDQ�GHULYH�WKH�JURXS�YHORFLW\�IURP�6FKRHQEHUJ�DQG�0XLUV�(TXDWLRQ��DV�IROORZV�

C33 =m

g + EN

l + 2m( ) 1 -l + 2mHk N

Î

Ð Ï Þ

à ß (2.18)


( )ßà

ÞÏÐ

Î +-

ßà

ÞÏÐ

Î +-+

===1

1

HIIHII +8

+&98

kml

rkml

ml

r ��

�

��

�� (2.19)

Equation 2.19 gives the same group-velocity expression as Equation 2.17. This

shows that Schoenberg and Muir’s effective-medium theory is equivalent to Pyrak-

Nolte’s low-frequency limit. Moreover, because Hudson’s first-order theory is

equivalent to Schoenberg and Muir’s model, it should also be consistent with Pyrak-

Nolte’s low frequency limit. This suggests that the inertial effect is indeed a

geometrical dispersion effect, and that we should be aware of it when the wavelength

is not long compared to the fracture geometry. For fracture size ranges from 1mm to

10m, the comparable wavelength 1mm to 10m corresponds to frequency range from

100 Hz to 10 6 Hz. Below 100 Hz, i.e., in the seismic frequency range, the inertial

effect can be ignored.

��'LVFXVVLRQ

The construction of fracture models is important for fracture characterization from

rock mechanical properties such as elastic-wave velocity. We proved that the first-

order Hudson’s model, Schoenberg and Muir’s model, and the low-frequency limit of

Pyrak-Nolte’s model are mathematically equivalent in the first order. This tells us

that penny-shaped cracks and long parallel-wall fractures are seismically

indistinguishable. We need to rely on the geological observations to determine which

model is more suitable for seismic fracture characterization in the field.

The relationships among the three models enable us to take advantage of each of

them. We can transform Schoenberg and Muir’s description of fractures to Hudson’s

description, and conduct fluid substitution. We can also use Pyrak-Nolte’s description

of fractures to estimate the magnitude of the frequency dispersion effects when

seismic waves pass through fractured rocks.


��5HYLHZ�RI�)UDFWXUH�LQGXFHG�$QLVRWURS\�LQ�3��DQG�6�ZDYH

9HORFLWLHV

In this section, I review the formulas for P- and S-wave velocity/traveltime

anisotropy when the fractured rocks are described by Hudson’s model. These

relationships will be used in Chapter 4 for interpreting the observed seismic

anisotropy in terms of fracture density and the physical parameters of cracks.

2.3.1 Thomsen’s Anisotropic Parameters

Hudson’s penny-shape-crack model (1980, 1981, 1990, 1994) gives expressions

for the effective moduli in the form of

��

LMLMLM

HII

LM &&&& ++= (2.20)

where �

LM& ’s are the isotropic background moduli and �

LM& ’s, and �

LM& ’s are the first-and

second-order corrections that depend on the crack orientation, crack density, aspect

ratio, and the properties of crack-filling materials. The crack density H is defined as:

paf

�� == D

91

H (2.21)

where a is crack radius, N/V is the number of cracks per unit volume, f is crack-

induced porosity, and a is aspect ratio. Rocks containing one set of parallel cracks

with their normals along the 3-axis show transverse isotropic symmetry. The first-

order corrections Cij1 ’s are defined in Equations (2.3) to (2.5) where l and m are the

Lamé constants of the unfractured rock. If the anisotropy is weak (Thomsen, 1986),


the fracture-induced anisotropy can also be expressed in terms of Thomsen’s

anisotropic parameters e , g , and d , as follows:

( )H

8&&&

mlml

e�

��

�

��

��

++

-

=

H8

&&&

��

��

�� -

=g

( ) ( )( ) H88

&&&

&&&&ÜÜÝ

ÛÌÌÍ

Ë+

- -

--+=

��

��

�

��

�

��

��

�� ml

md ��

&RPELQLQJ� (TXDWLRQ� �� DQG� WKH� 3�� DQG� 6�ZDYH� YHORFLW\�WUDYHOWLPH� DQLVRWURS\

IRUPXODV�LQ�WHUPV�RI� e �� g �� DQG� d �� ,�VKRZ�WKH�IUDFWXUH�LQGXFHG�YHORFLW\�WUDYHOWLPH

DQLVRWURS\�IRUPXODV�LQ�6HFWLRQV��DQG��

2.3.2 P-wave Velocity/Traveltime Anisotropy

In transversely isotropic media with a horizontal symmetry axis (TIH), the P-

wave velocity depends on both incidence angle q and azimuth f . The P-wave

group velocity was given by Sena (1991) in terms of e , g , and d , as follows:

( ) ��

�

�

��VLQVLQ

-

++ qq DDD99SS

(2.23)

e��

-=D

( ) fde �

�FRV�� -=D

( ) fde �

�FRV�� +-=D

where �S

9 is the P-wave velocity along the elastic symmetry axis. When there are

parallel vertical fractures in the rock, the elastic property of the rock is transversely


isotropic with a horizontal symmetry axis (TIH). P-wave velocity for P-waves

propagating parallel to the fracture plane is the fastest, and that perpendicular to the

fracture plane is the slowest. Based on Equation 2.23, Chen (1995) derived the P-

wave velocity/traveltime anisotropy

( ) ( ) ( )qfde �� VLQFRV� - D

D

3

3

3

3

99

77

(2.24)

where 3

9 is the average P-wave velocity, 3

9D is the fracture-induced velocity

variation, 3

7 is the total two-way traveltime in the interval between two events, and

37D is the traveltime lag generated in this interval. Equation 2.24 applies to small-to-

moderate incidence angle as large as 30 degree (Chen, 1995). Combining Equations

2.22 and 2.24, we get the fracture-induced P-wave velocity/traveltime anisotropy in

terms of the physical parameters of cracks:

( ) ( )qfmlml �� VLQFRV

��

ÜÜÝ

ÛÌÌÍ

Ë++

D

D

H88

7

7

9

9

3

3

3

3 (2.25)

where U1 and U3 are given in Equations 2.4 and 2.5.

Equation 2.25 shows that, at a fixed incident angle, the P-wave traveltime

between two horizontal reflectors is a cosine curve of the azimuth. Because U1

andU3 depend on the crack physical parameters, traveltime azimuthal variation is a

function of crack density, aspect ratio, and crack-filling material.

2.3.3 S-wave Velocity/Traveltime Anisotropy

In rocks containing vertical parallel fractures, vertically propagating shear-waves

split into a fast shear-wave polarized parallel to the fracture plane, and a slow shear-


wave polarized perpendicular to the fracture plane. Because shear-waves are not

sensitive to pore fluids, the traveltime lag between the fast and slow events is only

related to the fracture density.

In weak anisotropic environments (Thomsen, 1986), the traveltime anisotropy

induced by vertical parallel fractures can be expressed as:

��

��

�&&&

9V9V

77

6

6-

= D

=D

g (2.26)

Combining Equations 2.22 and 2.26, we get

��

��

��

��

��H

0

0HH8

&

&&ÜÜÝ

ÛÌÌÍ

Ë-

=ßà

ÞÏÐ

Î++

= -

=mml

mlm

mg (2.27)

where 0 is the P-wave modulus, and ml �+=0 . Combining Equations 2.26 and

2.27, we get the expression for the crack density H as a function of the shear-wave

velocity/traveltime anisotropy,

6

6

6

6

77

77

00

HD

ÜÝÛ

ÌÍË

-+=

D-=

sm

��

��

��

(2.28)

where s is the Poisson’s ratio of the unfractured rock. We can make a few

observations of equation (2.28):

1) fracture-induced shear-wave velocity/traveltime anisotropy is proportional to the

crack density;

2) fracture-induced shear-wave velocity/traveltime aniostropy is not affected by

crack-filling fluids;


3) for the same amount of shear-wave anisotropy, the larger the Poisson’s ratio of the

unfractured rock, the larger the crack density estimation.

Equations 2.25 and 2.28 give the P- and S-wave velocity/traveltime anisotropy as

functions of crack density and cracks’ physical properties. They will be used in

Chapter 4 to interpret the measured velocity/traveltime anisotropy in seismic P- and

S-wave data in terms of fractures.

��)UDFWXUH�,QGXFHG�$QLVRWURS\�LQ�3�ZDYH�5HIOHFWLYLW\

2.4.1 Abstract

This section analyzes the relationship between fracture-induced P-wave

reflectivity anisotropy and the physical parameters of the fracture network. These

parameters include crack density, aspect ratio, and filling fluids, as well as the

embedding rock moduli and the seismic-wave frequency. By combining the

analytical reflectivity formula for weakly anisotropic media given by Rueger with the

penny-shaped crack model developed by Hudson and Thomsen, I show the equations

for P-wave reflectivity induced by vertical parallel fractures under both high-

frequency (relative to the squirt-flow relaxation time) and low-frequency conditions.

My synthetic modeling shows three main conclusions:

1) reflectivity anisotropy increases with crack density and fracture-filling fluid bulk

modulus, and decreases with crack aspect ratio;

2) under high-frequency conditions, it decreases with the background rock’s Poisson’s

ratio;

3) the same fracture set induces more reflectivity anisotropy under high-frequency

conditions than under low-frequency conditions.

7R�DSSO\�WKHVH�UHVXOWV��,�SUHGLFW�WKH�UHIOHFWLYLW\�DQLVRWURS\�DW�D�YDULHW\�RI�UHDOLVWLF

VKDOH�VDQGVWRQH�LQWHUIDFHV�FDXVHG�E\�SHQQ\�VKDSHG�FUDFNV�LQ�WKH�VDQGVWRQH�


2.4.2 Introduction

Aligned fractures induce anisotropy into rock mechanical properties. To relate

the anisotropy to the fracture network configuration, various effective media models

can be used; for example, the penny-shaped crack models (Hudson, 1981, 1990;

Thomsen, 1995) and the slip-interface models (Schoenberg and Muir, 1989). Once

we have the effective moduli of fractured rocks, we can calculate the seismic

reflectivity at the boundary of the fractured rocks. For this calculation, I solve the

Zoeppritz equations in anisotropic media using the numerical method given by Keith

and Crampin (1977) or Rueger’s (1995, 1996) weakly anisotropic approximation.

This section analyzes the relationship between reflectivity anisotropy and fracture

physical parameters, as well as pore fluid and rock properties. The penny-shaped

crack models are used for both high-frequency and low-frequency conditions (Mavko

and Jizba, 1991; Mukerji and Mavko, 1994; Thomsen 1995).

For realistic applications, I use the velocity and density data of adjacent shale and

sandstone sets collected by Castagna and Smith (1994) as the embedding rock

properties. I categorize the sandstones into four classes, according to their isotropic

AVO behavior (Shuey, 1985; Rutherford and Williams, 1989; Castagna and Swan,

1997), and analyze the fracture-induced anisotropy superimposed on the isotropic

AVO for the four classes of gas sands and the corresponding brine sands.

2.4.3 Analytical Solutions

To show the analytical expressions of P-wave reflectivity at the boundaries of

fractured rocks, I combine the elasticity theories of fractured rocks and the analytical

expressions of P-wave reflectivity in weakly anisotropic media.


Review of Elasticity Theories of Fractured Rocks

Subsurface fracture networks can have various configurations, and each fracture

can have a unique geometry. The elastic properties of a full fracture network are by

far too complicated to be described with present-day techniques. To show the

relationship between the statistical average of fracture properties the fractured rock’s

elastic behavior, various elastic models have been suggested (Hudson, 1981, 1990;

Schoenberg and Muir, 1989; Thomsen, 1995). While these models are conceptually

different, many of the resulting elastic behaviors can be shown to be equivalent (Teng

and Mavko, 1995), as we discussed in Section 2.2. I chose to use the penny-shaped

crack models, which work well when the wavelength is long compared to the crack

size, and which allow us to explore the influence of pore fluids and crack geometry

on P-wave reflectivity.

In a later part of this section, I will specifically address the frequency dependence

associated with pore fluids. Seismic waves passing through the rock induce spatial

variation of pore-fluid pressure. When the wave frequency is too high for the fluids

in the thin fractures and the equant pores to reach pressure equilibrium, or if the

fractures are sealed for fluid flow, we call this a high-frequency condition. Hudson’s

(1981, 1990) penny-shaped crack model describes the high-frequency conditions,

because each crack is treated as isolated with respect to flow. When the wave

frequency is low and the pore fluids reach pressure equilibrium, we call this a low-

frequency condition. The elastic behavior of fractured rocks under low-frequency

conditions can be modeled by Thomsen’s (1995) low-frequency penny-shaped crack

model, or by the anisotropic fluid-substitution theories for low-frequency conditions

(Brown and Korringa, 1975; Mukerji and Mavko, 1994).

An advantage of penny-shaped crack models is that, in describing the fracture-

network configuration, they use physically intuitive parameters, including crack

density, aspect ratio, and filling fluid. The crack density H is defined as


��paf

�� FD

91

H == ��

where N/V is the number of cracks in a unit volume, D is the crack radius, a is the

crack aspect ratio, and F

f is the crack porosity. When the fractures are parallel with

their normals along the 3-axis (vertical direction), the rock is transversely isotropic

with a vertical symmetry axis (TIV). Under high-frequency conditions, the rock

elastic moduli can be calculated by Hudson’s first-order weak inclusion theory:

��

,-,-,-&&& += ��D�

ZKHUH

�

�

�

��H8&

ml

-=

( )�

�

��

�H8&

mmll +

-=

( )�

�

�

��

�H8&

mml +

-=

�

�

��H8& m-=

C661 = 0

( )08

+++

=��

��

� mlml

( )kmlml

+++

=��

��

8

��mlmpmlm

++

=D

0

( )[ ]��

��mlmp

mlmk

+++

=D

.

��E�


with l and m being the Lamé constants of the unfractured background rock, and K’

and m the bulk and shear modulus of the inclusion material. The inclusion is a fluid

with bulk modulus I. , I.. = , and �=m .

For low-frequency conditions, I use Thomsen's equations in terms of the

anisotropic parameters e , g , and d (Thomsen 1986):

( )( ) H

(

('

.

.

&

&&FL

I

ßà

ÞÏÐ

Î--

ÜÜÝ

ÛÌÌÍ

Ë-=

-=

�

�

��

��

��

��

� nn

e

( )( )H&

&&

��

��

��

��

� nn

g--

=-

=

( ) ( )( ) ( ) g

nn

end ÜÝÛ

ÌÍË

--

--=-

--+=

��

��

��

�

��

�

��

&&&&&&&

� ��D�

ZKHUH

( )�

��

-

Ôã

Ôâá

ÔÓ

ÔÒÑ

ßßà

Þ

ÏÏÐ

Î+ÜÜ

Ý

ÛÌÌÍ

Ë-+-= H$..

.

.

.

.OR' F

VW

I

V

I

FL nf

( ) ÜÜÝ

ÛÌÌÍ

Ë--

=

�

��

��

nn

nF

$ ��E�

In Equations (2.31a) and (2.31b), "lo" stands for low-frequency condition; . , ( , and

n are the bulk modulus, Young's modulus, and Poisson's ratio of the unfractured

background rock; Wf denotes the total porosity; and the subscript/superscript *, s, and

f denote the properties of the corresponding dry rock, solid grain, and pore fluids,

respectively. Thomsen (1995) also gives the expression of FL

' under high-frequency

conditions:


( ) ( )( )

�

��

��

-

Ôã

Ôâá

ÔÓ

ÔÒÑ

ßßà

Þ

ÏÏÐ

Î

-

-+-=

..

..H$

.

.

.

.PK'

I

VI

F

F

I

V

I

FL fn ��F�

and shows that this agrees with Hudson’s model. "mh" stands for moderate high

frequency, i.e., high-frequency conditions, but ones that is not yet high enough to

generate significant Raleigh scattering effect (Thomsen , 1995).

Review of P-wave Reflectivity in Isotropic and Weakly Anisotropic Media

Recall the isotropic AVO formula given by Shuey (1985):

( )( )

( ) ( ) ( )[ ]qqaa

qss

q ��

��VLQWDQ

��

VLQ�

-D

+ßà

ÞÏÐ

Î

-D

++== 33,623

5$55

( )ss

--

+-=�

��

�%%$

( )( ) ( )rraa

aa��

�

D+DD

=% ��D�

where

( )( )( ) ��

��

��

��

��

��

rrr

bbb

aaa

+=

+=

+=

��

��

��

rrrbbbaaa

-=D-=D-=D

��E�

and a , b , r ands are the P- and S-wave velocities, density, and Poisson’s ratio,

respectively. The isotropic reflectivity has two terms: the first term is the normal

incidence reflectivity, i.e., AVO intercept; the second and third terms are the AVO

gradient terms. At near offset, the third term can be ignored, and the AVO curve

increases with q�VLQ .


In anisotropic environments, the reflectivity can be solved by the Zoeppritz

equations, or by use of the weakly anisotropic approximation given by Rueger (1995,

1996). When the fractures are vertical and parallel, and have normals along the 1-

axis as shown in Figure 2.1, the fractured rock is transversely isotropic with a

horizontal symmetry axis (TIH). Using a perturbation method, Chen (1995) and

Rueger (1996) developed the formula for reflectivity in TIH media:

( ) ( ) ( )fqqfq ��$1,623,6233

555--

+=

( ) ( ) ( ) +ßßà

Þ

ÏÏÐ

ÎDÜ

ÜÝ

ÛÌÌÍ

Ë+D=

-

qfgab

dfq �� VLQFRV�

��

� 9

$1,6235

( ) ( ) ( ) ( ) ( )[ ] ( ) ( )qqffdfe �� WDQVLQFRVVLQFRV�� 99 D+D ��D�

The parameters ��9e and ��9d are the anisotropic parameters in the TIH media. They

can be related to Thomsen’s parameters in TIH media by

( )

ee

e��+

-=9

( ) ( )( )( )xee

xeedd

��

+++-

=9

�

�

�

��ab

x -= ��E�

The vertical P-wave velocity a and the vertical velocity of the S-wave polarized

parallel to the fracture plan b in Equation (2.33a) are defined as

eaa ��

+=

gbb ��

+= ��F�


where �

a and �b are the unfractured rock P- and S-wave velocities.

90

0

e1

e2

1

3

2

Figure 2.1: Reflection at the boundary between two fractured layers. The fractures are in the 90�

azimuth plane with their normals pointing in the 0� azimuth direction.

P-wave Reflectivity at a Boundary of Fractured Rock

When the source of anisotropy in both the upper and lower media is vertical

parallel fractures with their normals along the 1-axis direction, the reflectivity under

high-frequency conditions can be related to the fracture’s physical parameters. I

combine and simplify Equation (2.30) from Hudson’s model and Equation (2.33)

from Reuger’s weakly anisotropic reflectivity approximation:

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To evaluate the reflectivity of low-frequency conditions, I use Equation (2.33a)

where Thomsen’s anisotropic parameters are given by Equation (2.33b). The

combined form cannot be simplified as in Equation (2.34).

To check the accuracy, I consider a simple case in which the only source of

anisotropy is one set of vertical parallel fractures in the lower medium. I assume that

these fractures can be modeled by penny-shaped cracks. The upper medium is

isotropic with zero crack density. Hence, we don’t need to consider the anisotropic

radiation pattern and anisotropic attenuation, and can attribute the P-wave amplitude

anisotropy solely to the reflectivity anisotropy.

As an accuracy check, the weakly anisotropic solution is compared with the

Zoeppritz solution. The two solutions are compared in polar plots for all azimuths

(Figure 2.2a) and cross-section plots for 0� and 90� azimuths (Figure 2.2b). I choose

the crack density to be 0.08, aspect ratio to be 0.01, and fracture-filling fluid to be

brine (bulk modulus 2.8GPa, density 1.0g/cm3) under high-frequency conditions.

Figure 2.2 shows that at a small (<35�) incident angle, the Zoeppritz equation solution

is well approximated by the analytical approximation. At a large incident angle, the

approximation no longer works well. Because the first term of Equation (2.34a)

dominates at near offset, the reflectivity anisotropy roughly increases with q�VLQ , and

reaches its peak and trough at 0� and 90� azimuths, as shown in Figure 2.2a. The

peak-trough difference at the 30� incident angle Rp(q=30,f=0)-Rp(q=30,f=90) will

be used to represent the magnitude of reflectivity anisotropy.


Using Equations (2.29) to (2.34), I calculate the reflectivity anisotropy for various

parameters as follows:

crack density range: 0-0.1

crack aspect ratio range: 0.00001-0.1

crack-filling fluids: brine (bulk modulus 2.8 GPa, density 1.0 g/cm3)

oil (bulk modulus 1.6 GPa, density 0.88 g/cm3)

gas under 0.1MPa and ��R& (near the surface)

gas under 15MPa and ��R& (@1.5 km depth)

gas under 30MPa and ��R& (@3 km depth)

matrix rock Poisson’s ratio: 0.1-0.4

wave frequency: both low and high

For natural gas (the specific gravity of methane is 0.56), the bulk modulus and

density under various pressures and temperatures can be estimated with Batzle and

Wang’s (1992) empirical formula.

Figure 2.3 shows the reflectivity anisotropy as a function of crack density for

various fluids under both high-frequency and low-frequency conditions. I notice

these results: 1) the reflectivity anisotropy increases with crack density except at very

low crack density under low-frequency conditions; 2) the reflectivity anisotropy

under high-frequency conditions is larger than that under low-frequency conditions;

3) stiffer fracture-filling fluids give a larger reflectivity anisotropy than softer fluids;

4) reflectivity anisotropy increases with temperature and pressure when the crack-

filling fluid is gas; and, 5) the reflectivity anisotropy under high-frequency

conditions is more sensitive to the gas pressure change and less sensitive to stiffer

fluids’ bulk modulus change (brine vs. oil) than that under low-frequency conditions.

Figure 2.4 shows the reflectivity anisotropy as a function of crack aspect ratio.

The thinner the cracks, the larger the reflectivity anisotropy. This effect is obvious

under high-frequency conditions, especially for gas-filled cracks. It is negligible

under low-frequency conditions.


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Figure 2.3: Reflectivity anisotropy versus crack density in a fractured rock at the interface between an

isotropic rock with Poisson’s ratio 0.3 and the fractured rock with Poisson’s ratio 0.2. The

reflectivity anisotropy is represented by Rp(30,0)-Rp(30,90), i.e. the reflectivity difference

between 0� and 90� azimuths at 30� incident angle. The fractured rock contains a set of vertical

parallel fractures with crack density 0.08, aspect ratio 0.01, and various filling fluids under high-

frequency conditions (solid lines) and low-frequency conditions (dashed lines).


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Figure 2.4: Reflectivity anisotropy versus crack aspect ratio at the interface between an isotropic rock

with Poisson’s ratio 0.3 and a fractured rock with Poisson’s ratio 0.2. The fractured rock contains a

set of vertical parallel fractures with crack density 0.08, and various filling fluids under high-

frequency conditions (solid lines) and low-frequency conditions (dashed lines).

Figure 2.5 shows that, under high-frequency conditions, the reflectivity anisotropy

decreases with the Poisson’s ratio. Under low-frequency conditions, the reflectivity

anisotropy depends not only on the Poisson’s ratio of the embedding rock, but also on

the moduli of the solid grains, dry rocks, and porosity, as shown in Equation (2.31).


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Figure 2.5: Reflectivity anisotropy versus Poisson’s ratio of a fractured rock at the interface between an

isotropic rock with Poisson’s ratio 0.3 and the fractured rock with specified Poisson’s ratio. The

fractured rock contains a set of vertical parallel fractures with crack density 0.08, aspect ratio 0.01,

and various filling fluids under high-frequency conditions.

2.4.4 Reflectivity at Shale-Sandstone Interfaces

For realistic examples, I use the 25 sets of P-, S-wave velocity and density data

collected by Castagna and Smith (1994) as the rock matrix properties. The fracture-

induced reflectivity anisotropy superimposed on the isotropic AVO curves were

predicted for reflections at the shale/sandstone interfaces.

Isotropic AVO Classification

Figure 2.6 shows the P-wave velocity versus S-wave velocity for the sands.

When the fluid in the sandstone changes from gas to brine, that change may increase

or decrease the S-wave velocity, but it uniformly increases the P-wave velocity

because the fluid increases the bulk modulus of a rock more than it does the density.

This condition may lead to the reduction of impedance contrast between shale and


sandstone, and hence also reduce the absolute values of normal incidence reflectivity,

especially for rocks with large porosity.

According to their AVO behavior, the 25 sets of gas sands are categorized into

four classes (Rutherford and Williams, 1989; Castagna and Swan, 1997), as shown in

Figure 2.7. To show the fluid-substitution effects on AVO, I plot the corresponding

brine sands with the same shapes of symbols. For Class I tight gas sandstones, fluid

substitution with brine mainly moves the normal incidence reflectivity to the positive

direction; for Class III and IV loosely consolidated sands, it reduces the absolute

values of the normal incidence reflectivity as well as changes the AVO gradient. The

AVO behavior of shale-brine sandstone follows a linear trend passing through the

origin. These effects agree with what Castagna and Swan (1997) proposed.

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Figure 2.6: P- versus S-wave velocity for the gas sands and brine sands collected by Castagna and

Smith (1994). Notice the increase in P-wave velocity from the gas sands to the adjacent brine

sands.


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Figure 2.7: Classification of the gas sands (open symbols) based on the AVO behavior. The

corresponding brine sands (solid symbols) and its AVO background trend (dashed line) proposed

by Castagna and Swan (1997) are also shown in the graph. Notice that the fluid substitution from

gas to brine moves the AVO normal incident reflectivity and gradient towards the background

trend.

Fracture-Induced Anisotropy in Reflectivity

I assume that the only source of the azimuthal anisotropy is a set of vertical

parallel fractures in the sandstones. The possible anisotropy in the overburden shale

is transversely isotropic, and will not affect the reflectivity azimuthal variation.

When I calculate the reflectivity anisotropy at the 25 shale-sand interfaces, I

assume that the fractures are vertical and parallel, with a crack density of 0.08 and

aspect ratios of 0.001 and 0.1, respectively. The fluids in the fractures are the same as

those in the rock matrix. The calculated reflectivity anisotropy under both high-

frequency conditions and low-frequency conditions are shown in Figure 2.8. The

relationships between the reflectivity anisotropy and the various fracture and

embedding-rock parameters are summarized as follows:


1. Under high-frequency conditions, the reflectivity anisotropy decreases as the

embedding rock Poisson’s ratio increases. But there is no distinct range of

Poisson’s ratio that separates different sandstone classes. Hence, there is no

distinct range of reflectivity anisotropy for different sandstone classes. Under

low-frequency conditions, the reflectivity anisotropy as a function of Poisson’s

ratio does not have a linear pattern, because of the influence of other parameters,

including total porosity, grain bulk modulus, and dry rock moduli.

2. The clusters of different fluid types (gas vs. brine) are distinguishable under both

high-frequency and low-frequency conditions. However, gas-saturated cracks in

gas sands may give higher or lower reflectivity anisotropy than brine-saturated

cracks in adjacent brine sands. This depends on the tradeoff between the fracture-

filling fluid effect on reflectivity anisotropy and the matrix-fluid effect on

Poisson’s ratio, which affects the reflectivity as discussed earlier.

Because the change in pore pressure affects the bulk modulus of the fracture-

filling gas, it also influences the reflectivity. However, as we see in Figure 2.8,

the pore pressure effect is significant only for very thin cracks (aspect ratio 0.001)

under high-frequency conditions.

3. By comparing Figure 2.8a to 2.8c, we see that thinner cracks can give larger

reflectivity anisotropy under high-frequency conditions; and by comparing Figure

2.8b to 2.8d, we see that the aspect-ratio impact is negligible under low-frequency

conditions.


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Figure 2.8: Reflectivity anisotropy versus Poisson’s ratio at the shale/sandstone interfaces. The

reflectivity anisotropy is expressed as the reflectivity difference between 0� and 90� azimuths at

30� incident angle. The background rocks include the four types of gas sands (open symbols for

atmospheric pressure and gray symbols for high pressure) and corresponding brine sands (solid

black symbols). The overburden shale is assumed to be unfractured, and the sandstones contain a

set of vertical parallel fractures with crack density 0.08. The reflectivity anisotropy is induced a)

by the cracks with aspect ratio 0.001 under high-frequency conditions; b) by the cracks with

aspect ratio 0.001 under low-frequency conditions; c) by the cracks with aspect ratio 0.1 under

high-frequency conditions; d) by the cracks with aspect ratio 0.1 under low-frequency conditions.


2.4.5 Discussion

The results of reflectivity modeling show that the P-wave reflectivity anisotropy

is a function of crack density, aspect ratio, filling-fluid bulk moduli, embedding-rock

Poisson’s ratio, and wave frequency. In some situations, we should consider the

correlation of various physical parameters. For example, the fluid in the fractures is

often the same as the fluid in the rock matrix. Therefore, there is a tradeoff between

the fracture-filling fluid’s impact on reflectivity anisotropy and the matrix-fluid

impact on Poisson’s ratio and reflectivity anisotropy.

There are more issues that should be taken into account in the field analysis of

reflection amplitudes. On one hand, anisotropic attenuation and anisotropic radiation

pattern ought to be compensated before reflectivity anisotropy is analyzed; on the

other hand, other factors, depending on the in-situ environments, should be

considered. These include the fluid saturation, fluid mixture, high-pressure

compartments, and depth-related lithology change. Other models (Schoenberg and

Muir, 1989) are also used in the analysis of fracture-induced anisotropy (Sayers and

Rickett, 1997). The suitability of one model over the other depends on which one

better describes the in-situ fractures.

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60

CHAPTER 3

RESERVOIR ROCK PROPERTIES OF

FORT FETTERMAN SITE

3.1 Introduction

In this chapter, I analyze the well-log data, and gather the typical rock properties

at the reservoir level; these properties include the P- and S-wave velocities, density,

clay content, pore fluids, evidence of overpressure, and fractures. The main goal is

for this information to assist the next chapter's fracture interpretation, which uses

seismic anisotropy. Understanding the basic rock properties is also an integral part of

understanding the fractured environments.

The data to which I apply and test the fracture-induced anisotropy theories are

from the Fort Fetterman site. It is located at the southwestern margin of the Powder

River Basin, north of the town of Douglas, in Converse County, east central

Wyoming. A review of the regional geological framework can be found in the

appendix. Oil and gas have been produced from the Upper Cretaceous Niobrara and

Frontier Formations. Because of the low permeability of the reservoir rocks,

fracturing is an important reservoir component related to economical production.

To understand the subsurface fracture network, log data and multi-component

seismic data were collected. Because the seismic anisotropy is a combined effect of

the characteristics of the matrix rock, pore fluids, fractures, and seismic wave

Chapter 3 - Reservoir Rock Properties 61

frequency, we need to analyze and understand the physics of the formation rocks and

pore fluids before we can make any sense of the seismic fracture interpretation.

3.2 Overview of Well Logs at the Survey Area

Fort Fetterman field has decades of producing history. As shown in the basemap

in Figure 3.1, a 3D cube of P-wave data (GRI-3D) and two 2D lines of multi-

component data (GRI-1 and GRI-4) were collected at this field for the fracture study

sponsored by the Gas Research Institute. Most of well logs in the survey area were

available only in paper form. Digital well-log data were available from five wells as

listed in Table 4.1. Among them, the Red Mountain, the State #1-36, and the Wallis

wells have sonic log data that are crucial for the seismic study. Only the Red

Mountain well has, available for us, density logs along the whole depth range, while

the others have only segments of the density logs at the Niobrara and Frontier levels.

I analyzed, in this chapter, the logs mainly from the Red Mountain well.

Figure 3.2 shows the formation tops at these well locations. The target reservoirs

at the Niobrara and Frontier formations are marked on all three wells. The Niobrara

Formation consists of a series of fractured, marine chalks and limestones interbedded

with calcareous shales and bentonites. The Frontier Formation includes sand bodies

interbedded with marine shale. This formation ranges up to 1000 feet thick in central

and northeast Wyoming (Barlow and Haun, 1966). The uppermost sand body, the

first Frontier Sand, is a finely grained, "tight" sandstone with high acoustic velocities,

as observed in the sonic logs. A more detailed geological description can be found in

the appendix.


12345

8 9 10 11 12

123456

7 8 9 10 11 12

6 5

7 8

1234

9 10 11 12

13141516

21 22 23 24

25262728

33 34 35 36

123456

7 8 9 10 11 12

131415161718

19 20 21 22 23 24

252627282930

31 32 33 34 35 36

6 5

7 8

1718

19 20

2930

31 32

490092174300 Apache Corp. Spence 19830409

490090528800 Reliance Oil Govt. 3816 19261212

490092187400 Apache Corp. State 13015 19810318

490092059900 Davis Oil Highland Flats 11850 19741110

490092197900 Czar Resources Czar-West 10953 19811209

490092195300 Czar Resources Czar Bennett 12832 19820429

490097000592 ARCO O&G Morton Ranch 14200

490092106700 Davis Oil Highland Flats 8675 19760208

490092038900 Davis Oil Sears-Federal 8701 19730628

490092082800 Davis Oil La Prele St. 8700 19750714

490092134600 Energetics Inc. State 8380 19780613

490090555700 TEXACO Inc. SIMMS 11800 19640526

49009054800 TEXACO Inc. Govt.-Hawks-A 12831 19640317

490092041900 Energetics Inc. -- 12772 19731129

490092166200 Apache Corp. Githens 12776 19801215

490092091500 IMPEL Corp. Wallis 14900 19751210

490092246400 EXXON Corp. Box Creek 13803 19850321

490090541900 Ackard John -- 200(?) 19320701

490092195800 Chinook Resources Lois 11724 19810924

490092193800 Chinook Resources Tina 9684 19820123

490092134700 Energetics Inc. Sims 12776 19781101

1300129

0

- - - - - - - - - - - - - - - - - -

- - - - - - - - - - - - - - - - - -

- - -

- - -

- - -

- - -

- -

- - -

- - -

- - -

- - -

- -

GRI-3D

GRI-4

GR

I-1

Vastar Rooster Rock #1-36H

Vastar Idarado #1-27H

ARCO Red Mountain #1-H

Figure 3.1: Base map of the Fort Fetterman site showing the locations of the 2D multi-component

seismic lines GRI-1 and GRI-4, the 3D survey area GRI-3D in gray, and the well location.


Figure 3.2: (a) Formation tops superimposed on the well logs from the Red Mountain well.


Figure 3.2: (b) Formation tops superimposed on the well logs the State #1-36 well. At this well, the

density data were estimated using Gardner's equation outside the region of the Niobrara Shale and

the 1st Frontier Sand.


Figure 3.2: (c) Formation tops superimposed on the well logs the Wallis well. At this well, the density

data were estimated using Gardner's equation outside the region of the Niobrara Shale and the 1st

Frontier Sand.

It is particularly worth mentioning that the Arco Red Mountain #1-H well, which

targeted fractured Niobrara and Frontier reservoirs, gives a wide range of log types.

A pilot hole (straight hole) was drilled first. The P- and S-wave sonic logs, dipole

shear logs, density logs, spectral gamma ray logs, and resistivity logs were recorded

along the pilot hole. Multi-component VSP data were conducted with the receivers in

the borehole, and the sources at four different surface locations. Details about the

VSP survey are explained in the next chapter. To intersect the fractures, a highly

deviated hole (horizontal well) was drilled after the pilot hole. Figure 3.3 shows its

trajectory. To obtain fracture images and bedding information, formation

MicroScanner Logs ran through the horizontal well. The direct observation of the


subsurface fractures gives us the fracture-number count as well as the fracture-

aperture information. Our main effort is focused on analyzing the data from this well.

Table 3.1. Five wells supplying digital well-log data.

Operator Well Name Location Digital Logs

Apache State

#1-36

T33N R71W s36 SP, GR, Density, Neutron,

Resistivity, Sonic (P only)

Vastar Idarado

#1-27H


Resistivity

Arco Red Mountain

#1-H

T33N R71W s35 SP, SpectralGR, Density,

Neutron, Resistivity, Sonic

(P and S),

Dipole Shear Sonic, FMS

Vastar Rooster Rock

#1-36H


Resistivity

Impel Wallis

#1


Resistivity, Sonic (P only)

3.3 Spectral Gamma-Ray Logs and Clay Content

I used the spectral gamma-ray logs along the Red Mountain well in my analysis

of the clay content of the rocks at the reservoir level: the Niobrara Formation and the

first Frontier Sand.

The usual gamma-ray log records the sum of radiation emanating from naturally

occurring uranium, thorium, and potassium. It is a good shale indicator because

shale, among the sedimentary rocks, has a high concentration of thorium and

potassium. However, it can be misleading in carbonate formations that have a high


(3.3a)

(3.3b)

Figure 3.3: (a) Well trajectories of the Red Mountain well showing both the vertical hole (pilot hole)and the highly deviated hole (horizontal hole); (b) Map view of the highly deviated hole showingthat its azimuth is about N155oE.


uranium content (Rider, 1991). Figure 3.4 shows the spectral gamma-ray logs

recorded along the Red Mountain well. We can clearly see that the high gamma-ray

values at the Niobrara Formation are mainly attributed to the uranium. This is

consistent with the geology of the Niobrara Formation, which has a high percentage

of chalk and calcareous shale that can be the source of the uranium radiation.

Therefore, the spectral gamma-ray log of thorium and potassium is more appropriate

for the clay-content analysis.

To derive the shale content, I adapt the shale Index given by Bassiouni (1994):

( ) ( ) ( )[ ] ( ) ( )[ ]cThKshThKcThKThKKThsh CCCCCCCCI −−= /log (3.1)

where ( )logC 's are the curve readings in the zone of interest, and ( )cC 's are the curve

readings in the cleanest formation, and ( )shC 's are those in pure shales. This shale

index is more representative than those using potassium only or thorium only,

because it is virtually independent of clay type (Bassiouni, 1994). The clay content

shV for pre-tertiary rocks is given below, as a function of the shale index:

)12(33.0 2 −= shIshV (3.2)

The Niobrara Formation and the first Frontier Sand belong to the upper

Cretaceous (pre-tertiary) stratigraphy. Their clay contents are derived according to

equations 3.1 and 3.2. Figure 3.5 shows the statistical distribution of the clay

contents. The Niobrara Formation has a mean value of clay content 34.3%, and a

standard deviation of 17.3%; the first Frontier Sand has a mean of 30.3%, and a

standard deviation of 20.8%. The high clay-content values require us, in our velocity

and density analyses, to treat the reservoir rocks as shaly formations rather than as

pure carbonate rocks or sandstones.


Figure 3.4: The spectral gamma ray logs recorded along the Red Mountain well showing from left to

right the sum of all gamma ray radiation, the cable tension, the thorium, urianium, and potassium

logs.

0 50 100 150 200 250 300 3500

20

40

60

80

100

Niobrara - Red Mountain

Count0 20 40 60 80 100

0

20

40

60

80

100

1st Frontier Sand - Red Mountain

Count

(a) (b)

Figure 3.5: Statistical distribution of clay content of (a) the Niobrara Formation and (b) the firstFrontier Sand.


It is worth mentioning that there are two other independent indicators of the clay

content: the spontaneous potential log and the separation between density-log

porosity and neutron-log porosity (Rider, 1991). The former is due to the different

self-potentials of shale and sandstone; and the latter is due to the fact that shale has

higher density as well as higher neutron-porosity values relative to sand. A detailed

explanation can be found in Rider (1991). Figure 3.6 shows the curves of the SP logs

and the product of bulk density and neutron porosity, next to the K-Th shale-index

curve. We can see that they resemble each other at most depth levels with local

dissimilarities near depth 10350 ft and 10850 ft. The resemblance demonstrates that

Equation 3.1 gives a good shale indicator. Since the SP logs record the combined

effect of shaliness, formation-water salinity, drilling fluid/mud resistivity, formation

permeability, and other factors, the local dissimilarities in the SP curve could be due

to formation or drilling fluid resistivity change, or permeability change.

3.4 Pore Fluids

Hydrocarbons have a higher electrical resistivity than those of brine and water.

The induction logs use this effect to detect hydrocarbons. Figure 3.7 shows the deep

induction logs expressed in resistivity. The Niobrara and Frontier formations have a

higher average resistivity than the formations above, and could contain hydrocarbons.

They were the drilling targets.

After the horizontal well was drilled, the producing interval at the Red Mountain

well was the Frontier Formation. The initial 24-hour testing production yielded 1068

Mcf. gas, 32 bbl. oil, and 3 bbl. water. The oil gravity in the API unit is 53. The gas-

oil ratio (GOR) based on the initial production record is 33,375 scf/bbl. I assumed

that the volume fraction of each fluid in the pore is the same as that in the production

record. In reality, the GOR at the surface could be different from the GOR at the

reservoir depth. More gas could be in solution in the reservoir. On production, gas


0 0.5 1 1.5 2

1 104

1.05 104

1.1 104

1.15 104

K-Th Shale Index

Ish_KTh

Dep

th (f

t)

SP (mv) RHOB*NPOR (g/cc*%)

-100 -50 0 50 100

SP

0 20 40 60 80 100

RHOB*NPOR

Figure 3.6: a)K-Th shale index; b) SP; c) the product of density and neutron porosity. Each curve is an

independent shale indicator, therefore, they resemble each other.


0 20 40 60 80

0

2000

4000

6000

8000

1 104

1.2 104

ILD (ohmm)

DE

PTH

(ft)

0 20 40 60 80

1.06 104

1.08 104

1.1 104

1.12 104

1.14 104

1.16 104

1.18 104

ILD (ohmm)

DE

PTH

(ft)

(a) (b)

Figure 3.7: ILD deep induction logs expressed as resistivity along the Red Mountain well. (a) showsthe entire depth range; (b) shows the zoomed in section at the reservoir depth.

comes out of solution. Therefore, there is an uncertainty in the reservoir fluid

properties. I assumed that this uncertainty is not significant since the GOR is very

high already. An even higher GOR will not make much difference on acoustic

properties.


To calculate the density and acoustic velocity of the fluid mixture, we also need to

know the temperature and pressure. At the depth of the first Frontier Sand, the rock

temperature and pore pressure estimated using the universal empirical formulae from

the Petrotool Software package are 183oF, and 5169 psi. Under this condition, the

fluid mixture has a density of 0.3 g/cc, and a velocity of 2000 ft/sec (0.6 km/sec).

However, a gas-producing formation often has a higher temperature and pore

pressure than the surrounding rocks. At the Powell-Ross Field in Converse County,

same county as the study area is located in, the temperature and pore pressure of the

Frontier reservoir is about 262oF and 8000 psi as listed by Hando (1976). Under this

condition, the gas-oil mixture will instead have a density of 0.33 g/cc and a velocity

of 2400 ft/sec (0.72 km/sec). The fluid density and velocity are required in porosity

calculation and fluid substitution calculation.

No fluid type record is available for the Niobrara Formation. Several attempts to

provide an accurate fluid content were not conclusive because of the high clay

content and low porosity. Therefore, for the velocity and density analyses in the next

section, I keep an open range of pore fluid type in the Niobrara Formation: from

100% brine to 100% gas.

3.5 Velocity and Density Analyses

The velocity and density logs recorded along the pilot hole of the Red Mountain

well give the isotropic elastic properties of the rocks at known depth levels. Getting

these properties is a necessary step toward the seismic anisotropy analysis. This

section analyzes the velocity and density logs along the Red Mountain well.

Figure 3.8 shows the statistics, based on the well logs from the Red Mountain

well, of the P- and S-wave velocities, density, and porosity of the Niobrara

Formation. The porosity calculation is based on the density log and uses the

following equation for shaly formations (Bassiouni, 1994):


( ) matrixshshshflb VV ρφρφρρ −−++= 1 (3.3)

where φ is the intergranular porosity, shV is the clay volume fraction, and bρ , flρ ,

shρ , and matrixρ are the bulk, fluid, shale, and matrix densities. Note that the

intergranular porosity in this context does not include the porosity in the clay

material, and should be lower than the apparent/total porosity. I assumed a matrix

density matrixρ of 2.71 g/cc, corresponding to that of a limestone, and a shale density

shρ of 2.60 g/cc, corresponding to the bulk density at a 100% clay content point

within the Niobrara Formation. The pore fluid in the Niobrara Formation, as we

discussed previously, can range from pure water to pure gas. The mean value and

standard deviation of each entry are given below:

Mean Standard Deviation

Vp 4.158 km/sec 0.265 km/sec

Vs 2.287 km/sec 0.148 km/sec

Density 2.50 g/cc 0.10 g/cc

Porosity (water) 9.95% 6.02%

Porosity (gas) 6.92% 4.19%

Velocities, density, and clay content are correlated properties. The cross plots of

P-wave velocity versus density, clay content, S-wave velocity, and Vp-Vs ratio are

shown in Figure 3.9. Within the Niobrara Formation, the density change, from 2.4

g/cc to 2.6 g/cc, is small compared to the clay-content change, from 0 to above 60%.

The P-wave velocity increases as the clay content drops, but shows no obvious

change with the density, simply because of the small density range. The S-wave

velocity increases with the P-velocity, and their relationship matches the Greenberg-

Castagna empirical relation (Greenberg and Castagna, 1992) for a 60%-limestone and

40%-shale mixture. The Vp-Vs ratio is about 1.8 for the Niobrara Formation.


Figure 3.8: Range of the P-, S-wave velocities, density, and porosity assuming the pore fluid is gas orwater based on the log measurement of the Niobrara Formation along the Red Mountain well.

0 100 200 300 400 500 600 7000

10

20

30

40

50

Porosity (water)

Count

0 50 100 150 200 250 300 3503.5

4

4.5

5

5.5

Vp

Count0 100 200 300 400 500

1.5

2

2.5

3

3.5

Vs

Count

0 100 200 300 400 500 600 7001.8

2

2.2

2.4

2.6

2.8

Density

Count0 100 200 300 400 500 600 700 800

0

10

20

30

40

50

Porosity (gas)

Count


1.8

2

2.2

2.4

2.6

2.8

3.5 4 4.5 5 5.5Vp (km/s)

0

20

40

60

80

100

3.5 4 4.5 5 5.5

Vp (km/s)

1.5

2

2.5

3

3.5

3.5 4 4.5 5Vp (km/s)

Shale Line

Limestone Line

40% Shale + 60% Limestone

1

1.5

2

2.5

3

3.5

3.5 4 4.5 5 5.5Vp (km/s)

Figure 3.9: Crossplots of the P-wave velocity versus density, clay content, S-wave velocity, and Vp-Vsratio for the Niobrara Formation. The data are based on the log measurements at the RedMountain well.


Figure 3.10 shows the velocity, density, and porosity statistics for the first

Frontier Sand. For the porosity calculation, I assumed a matrix density matrixρ of 2.65

g/cc as that of the quartz, and a shale density shρ of 2.60 g/cc corresponding to the

bulk density at a 100% clay content point within the first Frontier Sand. The pore

fluid is taken to be the fluid mixture with a gas/oil ratio of 33,375 scf/bbl as described

in the previous section. The porosity is calculated using Equation 3.3. The means

and standard deviations are summarized as follows:

Mean Standard Deviation

Vp 4.683 km/sec 0.146 km/sec

Vs 2.714 km/sec 0.166 km/sec

Density 2.56 g/cc 0.04 g/cc

Porosity (gas+oil) 3.05% 1.89%

The first Frontier Sand appears to have an extremely low porosity. If the matrix

is not pure quartz, but mixed with heavy minerals, the mean porosity can be

somewhat higher than the calculated 3.05%. Yet it is still a very tight formation, and

fracturing is a necessary factor for economical production.

The cross-plots of P-wave velocity versus density, clay content, S-wave velocity,

and Vp-Vs ratio of the first Frontier Sand are shown in Figure 3.11. The P-wave

velocity increases as the clay content drops, but shows no apparent relationship with

the density. The Vp Vs cross-plot shows a discrepancy between the log-based Vp-Vs

relationship and the Greensberg-Castagna prediction. This could be due to the

fracturing because the S-wave is more sensitive to fractures than the P-wave, and has

a lower velocity than the empirical prediction. The Vp-Vs ratio is about 1.7 for the

first Frontier Sand.

This analysis provides a baseline for the seismic fracture analysis. The log data

will be used to generate a synthetic seismogram that ties with the field seismic data,

and to model the AVO behaviors at the formation boundaries.


0 20 40 60 80 100 120 1404

4.5

5

5.5

Vp

Count0 20 40 60 80 100

2

2.5

3

3.5

Vs

Count

0 20 40 60 80 100 120 1402.2

2.4

2.6

2.8

Density

Count0 50 100 150 200

0

10

20

30

40

50

Porosity (oil+gas)

Count

Figure 3.10: Range of the P-, S-wave velocities, density, and porosity assuming the pore fluid is a gas-oil mixture with gas-oil ratio 33,375 scf/bbl based on the log measurement of the first FrontierSand along the Red Mountain well.


1.8

2

2.2

2.4

2.6

2.8

4 4.5 5 5.5Vp (km/s)

0

20

40

60

80

100

4 4.5 5 5.5Vp (km/s)

1.5

2

2.5

3

3.5

4 4.5 5 5.5Vp (km/s)

Shale Line

30% Shale + 70% Sandstone

Sandstone Line

1

1.5

2

2.5

3

3.5

4 4.5 5 5.5Vp (km/s)

Figure 3.11: Crossplots of the P-wave velocity versus density, clay content, S-wave velocity, and Vp-Vs ratio for the first Frontier Sand. The data are based on the log measurements at the RedMountain well.


3.6 Evidence of Overpressure

The generation, partial expulsion, and subsequent cracking of liquid hydrocarbons

in the Cretaceous sandstones and shales caused regional overpressure compartments

in the Powder River Basin (Surdam, et al., 1994). The elevated fluid pressure can

make the rocks more brittle and susceptible to fracturing. Therefore, finding the

evidence of overpressure helps to locate the fracture-prone regions.

During a normal compaction process, fluids in shale will be gradually squeezed

out as the burial gets deeper and deeper. This will correspond to a gradual increase in

the shale density, and a gradual decrease in shale conductivity. However, if the fluids

were trapped and could not get out during compaction, overpressure will occur

(Rider, 1991). The elevated fluid pressure will preserve more porosity, and break the

normal compaction trend of both the density logs and the conductivity logs. A lower

density and a higher conductivity than normal could mean an overpressure zone.

Figure 3.12 shows the conductivity log and the density log at the Red Mountain well.

Both curves break away from the normal compaction trend below 10500 feet depth.

This could indicate that the pore-fluid pressure of the Niobrara and Frontier

formations is higher than normal, and hence the rocks are more susceptible to

fracturing. This again substantiates the direct observations of fractures at the

Niobrara and Frontier levels.

3.7 Indirect Evidences of Fractures

Schafer (1980) proposed to use the comparison of density-log porosity with the

sonic-log porosity to identify fractured zones. When the sonic P-wave passes the

fractured rock, Fermat's principle implies that it chooses the fastest way from the

emitter to the receiver, and is not sensitive to the presence of fractures. In other

words, the P-wave mainly samples the matrix. The density log measures the bulk

density that contains both the intergranualar porosity and the fracture-induced


1880 1900 1920 1940

0

2000

4000

6000

8000

1 104

1.2 104

IRDP (mmho)

Dep

th (f

t)

1 1.5 2 2.5 3

Density (g/cc)

Figure 3.12: The conductivity log and the density log along the Red Mountain well. The normal

compaction trends are shown by the gray lines. Below the depth of 10500 ft, the conductivity is

higher than the trend, and the density is lower than the trend. It could indicate an overpressure

zone.


porosity, and should predict a lower porosity than the sonic-log porosity. On the

cross-plot of sonic wave traveltime and density, the same P-wave traveltime

corresponds to a lower density in a fractured zone than that in an unfractured zone.

Figure 3.13 shows the cross-plot of the sonic wave traveltime and the bulk density

of the Niobrara Formation based on the log data from the Red Mountain, the State #1-

36, and the Wallis wells. When the P-wave traveltime is below 70 µs/ft, most density

values are above 2.5 g/cc, indicating a dense rock. However, there are points that

have much lower density but high P-wave velocity. Most of these points are from

logs along the Red Mountain and the State #1-36 wells. It could be due to fractures.

Based on this graph, there are probably more fractures at the Red Mountain and State

#1-36 well locations than at the Wallis well location.

50

60

70

80

90

100

1.61.822.22.42.62.8

DT_Rm (us/ft)DT_St (us/ft)DT_Wl (us/ft)

Density (g/cc)

Red MountainState #136Wallis

FRACTURED?

UNFRACTURED

Figure 3.13: Cross-plot of P-wave traveltime versus density of the Niobrara Formations based on logs

from the Red Mountain, the State #1-36, and the Wallis wells. The points with high velocity but

low density could correspond to fractured intervals.


This indirect fracture indicator should not be used alone without other

confirmation of fracture occurrence because the cross-plot may be showing

lithological differences rather than the presence of fractures. One example showing

how incorrect inferences can be made can be found in Rider's book (1991).

3.8 FMS Logs and Fracture Number Count

The Formation MicroScanner (FMS) tools obtain oriented, high-resolution

imagery of electrical conductivity around the borehole wall with four arrays of button

electrodes (Schlumberger, 1989). The FMS tool has 1cm vertical resolutions and can

detect fractures 1cm apart. Two runs of FMS logs were conducted along the

horizontal borehole of the Red Mountain well: from 10850 feet to 11750 feet, and

from 11660 feet to 12970 feet. Figure 3.14 shows a segment of the FMS display.

The conductivity images measured by the four pads are displayed side by side. Two

vertical fractures with large apertures cutting through the borehole can be identified

easily at depth of approximately 12637 ft, and 12639 ft.

Arco scientists processed the two runs of FMS logs with a similar analysis

method using Schlumberger's FLIP/FRACVIEW software (Sovich, 1996, May et. al,

1996). I counted the fracture number within various aperture ranges and fracture

strike ranges based on their results, and show fracture number distributions in Figure

3.15. Several observations are summarized below:

(1) 93% of the fractures in the shallower depth range (10865 feet to 11750 feet) and

75% of the fractures in the deeper depth range (11750 feet to 12970 feet) are

trending along the N70oE ± 10o direction. This is the only one prevailing strike.

(2) The average horizontal spacing of large-aperture fractures (aperture > 0.2mm) is

about 3.2 feet in the shallower section, and 12.1 feet in the deeper section.

(3) Arco's FMS analysis shows more small-aperture fractures in the deeper depth

range than in the shallower depth range. I believe that this is a result of the

different processing accuracy for the two runs of FMS data. By comparing the


aperture distribution near the overlapping region of the shallower and deeper

depth ranges, I observed a sudden increase in the number of the small-aperture

fractures from the shallower to the deeper depth. Generally, the number of

fractures at a given aperture range will not change drastically unless it is across

the formation boundary. Since the overlapping region is not a formation

boundary, I believe that this change is mainly due to the different processing

accuracy for the two runs rather than the actual change.

(4) Except at very small apertures where the fractures are under-sampled, the

frequency of fractures with a given aperture decreases as the aperture increases.

This is consistent with Barton and Zoback's observation (1992) in the Cajon Pass

well. Whether the aperture distribution obeys the power law, as suggested by

Barton and Zoback (1992), is worth further analysis.

Figure 3.14: FMS display showing open fractures at the Frontier Formation level. Note that the FMSlogs ran along the highly deviated hole. The near-vertical fractures appear at low dip angle. Thebedding appears at high dip angles. The depth is the measured depth in feet along the boreholerather than the true vertical depth.


0

50

100

150

200

250

300

350

10 30 50 70 90 110 130 150 170

10850-11750 ft11660-12970 ft

Strike (degree relative to true North)

0

20

40

60

80

100

120

0.008 0.01 0.02 0.04 0.06 0.08 0.1 0.2 0.4 0.6 0.8 1 2 4

10850-11750 ft11660-12970 ft

Aperture (mm)

6

Figure 3.15: The distributions of fracture strike and aperture based on the FMS logs. The original

FMS data of the two runs (10850-11750ft & 11660-12970ft) were subjected to a similar analysis

by Arco's scientists. These number counts are based on Arco's plots. Note that only fractures

between 11750 to 12970 feet were counted for the second run from 11660 to 12970 feet due to the

data availability on Arco's plots.


3.9 Anisotropy in Dipole Sonic Logs

Dipole shear sonic logs record the waveforms of the shear waves emitted from

two perpendicular sources, and received by two perpendicular receivers. After Alford

(1986) rotation to the principle directions, i.e. parallel and perpendicular to the

fracture orientation, we get a fast and a slow shear waves polarized in the principle

directions. The traveltime lag between the fast and slow shear wave can be caused by

the fracture-induced anisotropy. The shear wave birefringence parameter is

calculated using:

TT

VV

S

S ∆≅∆≅∆=µµγ (3.4)

where γ is the shear wave birefringence parameter or the Thomsen shear-wave

parameter for weak anisotropy (1986), ∆ represents the difference between the fast

and slow shear waves, SV is the sonic shear velocity, T is the transit time, µ is the

shear modulus of the rock. Derivation of this equation can be found in Chapter 2.

The shear wave data were given to us after the Alford rotation done by ARCO,

Schlumberger, and Nolte and Cheng (1996) at M.I.T. Figure 3.16 shows the 10-feet

average values of the fast shear wave (S1) polarization azimuth, transit time,

birefringence parameter, K-Th shale index, and P-wave sonic velocity. Unlike the

tightly clustered fracture orientation observed the FMS data, the S1 polarization

wanders around between N40oE and N170oE, with a mean of N91oE and a standard

deviation of 24o. The shear wave birefringence parameter has a mean of 5.6%, and a

standard deviation of 6.9%.

Three main zones of shear wave splitting A, B, and C are marked on Figure 3.16.

Zones A and B are within the Niobrara Formation. Zone C corresponds to the first

Frontier Sand. A closer look at these three zones shows that the S1 azimuth stays

close to N80oE within these zones. This indicates that outside these zones where the


(a) (b) (c) (d) (e)

Figure 3.16: Dipole sonic log (a) fast shear wave azimuth; (b) traveltime of the fast and slow shear

waves; and (c) shear wave birefringence. Those plotted next to the dipole logs are (d) K-Th shale

index and (e) P-wave sonic velocity. Three main zones of shear wave splitting are marked by

Zone A, B, and C. Zone C corresponds to the first Frontier Sand.

birefringence is small, the uncertainty in the Alford rotation angle is probably large,

and causes the wandering of the S1 polarization direction. Within the first Frontier

Sand, the shear wave birefringence has a mean value of 7.6% and a standard

deviation of 4.8%.

Notice that both Zone B and Zone C have low clay content and high P-wave

velocity. Outcrop and core observations at the study site (May et al., 1996) show that

"all fractures, regardless of orientation, are better developed in thinner-bedded, well-

S1 S2

Zone A

Zone B

Zone C

0 10 20 30 40

Birefringence

0 0.2 0.4 0.6 0.8 1

Shale Index

Azimuth (deg) Birefringence (%)Travel Time (ms)

1st Frontier Sand

0 10 20 30 40

Ish_KTh Vp (m/s)

0 0.2 0.4 0.6 0.8 1 4000 5000

P-wave Velocity

100 125 150 175

Travel Time

100 125 150 175

1.06 104

1.08 104

1.1 104

1.12 104

1.14 104

1.16 104

0 45 90 135 180

Fast Shear Polarization


cemented lithologies and commonly terminate at thin shale or bentonite beds." The

dipole sonic log results are consistent with the outcrop observations. Furthermore, it

demonstrates that the dipole sonic logs and seismic surveys can be good fracture

detection tools.

3.10 Conclusions

In this chapter, I analyzed the log data and gathered information about clay

content, pore-fluid properties, formation velocities and density, and evidence of

overpressure and fractures at the Niobrara and Frontier levels. The clay content

analysis confirmed the prior geological information of the formations. The elastic

properties of rocks and pore fluids are essential for the seismic analysis in the next

chapter.

Natural fractures have been directly observed and measured on the FMS logs.

The prevailing strike of the fractures is N70oE at the Niobrara and Frontier levels.

The apparent aperture of fractures ranges from 0.008 mm to above 4mm. The

fracture frequency at a given aperture decreases as the aperture increases. The dipole

sonic logs show a fast shear wave polarization around N80oE in the zones where

shear wave splitting is comparatively large. This roughly agrees with the FMS

observations. The correlation between the main shear wave splitting zones and high

P-wave velocity, low clay content agrees with the outcrop and core observations

(May et al., 1996) that the fractures at the study site are better developed in tight

layers and tend to terminate at shale or bentonite beds.

Log measurements of fractures have the advantage of high depth resolution, and

the disadvantage of low area coverage. In order to get the subsurface fracture

information in the Fort Fetterman field, 2D multi-component and 3D P-wave seismic

surveys were conducted. In the next chapter, I will analyze the anisotropy in the

seismic data, and map the fracture distribution and properties over the survey area.


The log data will be used in conjunction with the seismic data to give a realistic

fracture property mapping.

3.11 References

Alford, R.M., 1986, Shear data in the presence of azimuthal anisotropy, SEG 56th

Annual Meeting Technical Program

Barlow, J. A., and Haun, J. D., 1966, Regional stratigraphy of Frontier Formation

and relation to Salt Creek field, Wyoming: AAPG Bulleting, 50, 2185-2196

Barton, C.A., and Zoback, M.D., 1992, Self-similar distribution and properties of

macroscopic fractures at depth in crystalline rock in the Cajon Pass scientific drill

hole, Journal of Geophys. Res., 97, No B4, 5181-5200

Bassiouni, Z., 1994, Theory, measurement, and interpretation of well logs, First

Printing, Society of Petroleum Society

Greenberg, M.L. and Castagna, J.P., 1992, Shear-wave velocity estimation in porous

rocks: theoretical formulation, preliminary verification and applications,

Geophysical Prospecting, 40, 195-209.

Hando, R. E., 1976, Powell-Ross Field Converse County, Wyoming, Twenty-eighth

American Field Conference, Wyoming Geological assoc Guidebook

May, J., Mount, V., Krantz, B., parks, S., Gale, M., 1996, Structural framework of

southern Powder River Basin: A geological context for deep northeast trending

basement fractures, Gas Research Institute research report

Nolte, B., and Cheng, C.H., 1996, Estimation of non-orthogonal shear-wave

polarizations and shear-wave velocities from four-component dipole logs, MIT:

borehole Acoustics & Logging; Reservoir Delineation Consortia Annal Report,

p2-1-2-20

Rider, M. H., 1991, The Geological Interpretation of Well Logs, Revised Edition

Schafer, J.N., 1980, A practical method of well evaluation and acreage development

for the natural fractured Austin chalk formation, Log Analyst, XXI(1), 10-23


Schlumberger, 1989, Log interpretation principles/applications

Sovich, J., 1996, ARCO Exploration and Production Technology Internal

Correspondence

Surdam, R.C., Jiao, Z.S., and Martinsen, R.S., 1994, The regional pressure regime in

Cretaceous sandstones and shales in the Powder River Basin, P. Ortoleva and Z

Al-Shaieb, eds., Pressure Compartments and Seals, Am. Assoc. Petro. Geol.

Memoir, 61, 213-233

Thomsen, L., 1986, Weak elastic anisotropy, Geophysics, 51, 1954-1966

91

CHAPTER 4

INTEGRATED SEISMIC INTERPRETATION OF

FRACTURE NETWORKS

4.1 Introduction

In this chapter, using the seismic datasets from the Fort Fetterman site, I explore

and test the feasibility and reliability of using P-wave anisotropy, in conjunction with

S-wave data and other available information, to characterize subsurface fracture

networks.

Shear-wave splitting techniques have been used successfully in detecting fractures

in many field examples. However, shear waves are not sensitive to the fluids in pores

and fractures. Seismic shear-wave data are rarely available in 3D. P-wave data are

cheaper to acquire, have higher signal-to-noise ratio, and are more readily available in

3D than are shear-wave data. However, the use of P-wave data in fracture detection

and characterization is not fully exploited.

At the Fort Fetterman site, various seismic surveys were conducted for the

fracture study. The available seismic data include the multi-component shear-wave

VSP data at the Red Mountain well location, two 2D lines of multi-component

seismic data, and a 3D cube of P-wave data. The 2D and 3D seismic survey map is

shown in Figure 3.1 in Chapter 3. The advantages of having different types of

surveys are that each survey samples different areas of the earth, and has different

Chapter 4 - Integrated Seismic Interpretation 92

resolutions. Moreover, the P- and S-waves sample different physical properties. P-

waves are sensitive to a change in fracture-filling fluids, but S-waves are not. VSP

data have direct time-to-depth correspondence because the depths of the downhole

receiver are known. 2D four-component shear-wave surveys allow us to map the

fracture distribution along the 2D lines. The anisotropy in 3D P-wave velocity and

amplitude makes it possible for us to identify the fracture-filling fluids, as well as to

map the fracture distribution over the larger 3D survey area. I analyze and interpret

the anisotropy in the VSP and the 2D S-wave velocities, and the 3D P-wave velocity

and amplitude, in Sections 4.2 to 4.5. Section 4.6 summarizes the integrated fracture

interpretation of this field, lessons learned, and the general applicability of these

methods.

4.2 VSP shear-wave birefringence and 1D fracture-density

distribution

Vertical seismic profiling (VSP) data consist of records from surface sources to

downhole geophones. They provide direct seismic ties of time to depth on a

relatively fine scale (Hardage, 1984). Multi-component shear-wave VSP data can

capture the fracture-induced anisotropy in the Earth at fine depth resolution. It has

been used successfully in fracture detection and orientation prediction (Queen and

Rizer, 1990; Winterstein and Meadows, 1991a, b).

At the Red Mountain well location, VSP data were collected with P- and S-wave

sources at four different offsets (Figure 4.1). For my fracture analysis, I used the

four-component shear-wave data with sources at 277-ft offset. This offset is much

smaller than the depth range from 1499.9 feet to 11500.5 feet, so the data can be

treated as approximately zero-offset VSP data. At the source location, there are two

perpendicular shear sources, S2 and S3. The S3 baseplate first motion is N36oE

relative to true north. This angle is the sum of the measured angle by magnetic

compass and the magnetic declination. The magnetic declination is +11o in Converse


County, Wyoming. The S2 baseplate motion is perpendicular to that of S3. As

shown in Figure 4.2, the sonde interval is approximately 500 ft between depths of

1499.9 ft and 7720 ft. Below 7720-ft depth, the average sonde interval is 67.5 ft.

The raw VSP data were recorded by a tri-axial geophone whose polarization

changes at each depth. Before conducting the Alford rotation, we must first rotate the

data such that the polarizations of the sources and receivers are in the same directions.

In the deep borehole, the orientation of the geophone can be determined by the far-

offset P-wave data. How to determine the downhole tri-axial geophone from the P-

wave data, and how to rotate the data to a desired coordinate system are beyond the

scope of this thesis. Details can be found in Greenhalgh and Mason (1995), and

Knowlton and Spensor (1996). This work was performed by ARCO. They rotated

the shear-wave data into the XY coordinates, where the X-direction is along N126oE,

and the Y-direction along N36oE, parallel to the S2 and S3 sources directions,

respectively.

273ft

71.3o

160o

N

Red Mountain Well

single P source

single P source

S sources

S sources

1759ft

2831ft

Figure 4.1: VSP survey map. The 273-ft near-offset VSP shear-wave data are used in the shear-wave

splitting analysis.


Figure 4.2: The 64 depth levels of the downhold geophone for the VSP survey. The sonde interval is

approximately 500 ft between 1499.9-ft and 7720-ft depth. Below this depth, the sonde interval is

much closer with an average of 67.5 ft.

Figure 4.3 shows the four S-wave components named XX, XY, YX, YY. The

first letter of each component name indicates the source direction, and the second

letter indicates the receiver direction after geophone orientation has been applied. If

the medium is isotropic, the shear-wave generated by the X source should be received

only by the X receiver, and the Y source by the Y receiver. Figure 4.3 shows strong

energy in the cross traces XY and YX. This energy indicates the existence of

subsurface anisotropy that causes shear-wave splitting during propagation.


Figure 4.3: The four VSP S-wave components XX, XY, YX, and YY before the Alford rotation. X is

in the N126oE direction, and Y is in N36oE direction. The strong energy in the mismatched traces

XY and YX indicates subsurface anisotropy.

To determine the natural-anisotropy symmetry directions of the subsurface rocks,

which often indicate the fracture orientation, I applied the Alford rotation (1986) to

the VSP shear-wave data. The procedure will rotate the source-receiver acquisition

direction from the XY directions to a new set of directions X'Y'. A single rotation

angle is applied to all VSP traces. The rotation angles that I tried range from 10o to

90o, with a step of 10

o. Figures 4.4 (a) to (d) shows the S-wave components after

Alford rotations of 20o, 30

o, 40

o, and 60

o, respectively. When the target X'Y'

coordinates are parallel to the symmetry planes of the fractured medium, the cross-

talk energy in X'Y' and Y'X' sections will be minimized. We can see that the rotation


of 30o gives the smallest cross-talk energy in X'Y' and Y'X' sections. The fast

direction X' (N96oE) is, therefore, the predicted fracture orientation. Figure 4.5

compares the S-wave traces received at depth level #61 after rotations of angles

ranging from 20o to 40

o, with a step of 1

o. There is no significant change over any

range of 10o or less. Therefore, I consider the uncertainty of the estimated fracture

direction to be about +/- 10o. May et al. (1996) point out that a set of N110

oE+/-15

o

fractures was observed in the Tertiary strata, and locally in the Cretaceous strata; a

set of N70oE+/-10

o fractures was observed in the Cretaceous, but not in the Tertiary

strata. The trend of N96oE fast-VSP-shear-wave direction is based on the rotation of

the data at all depth levels, and hence is the average fracture direction over both the

Tertiary and Cretaceous intervals. If we assume that the N70oE and the N110

oE

fractures generate equal amounts of anisotropy, the average anisotropy symmetry-

plane direction is along N90oE. The finding of the average fracture direction of

N96oE+/- 10

o at the Red Mountain well location is consistent with the geological

observations.


Figure 4.4: (a) The four VSP S-wave components X'X', X'Y', Y'X', Y'Y' after the Alford rotation of

20o.


Figure 4.4: (b) The four VSP S-wave components X'X', X'Y', Y'X', Y'Y' after the Alford rotation of

30o. The optimum rotation angle 30o corresponds to the minimum energy in X'Y' and Y'X'

components.


Figure 4.4: (c) The four VSP S-wave components X'X', X'Y', Y'X,' Y'Y' after the Alford rotation of

40o.


Figure 4.4: (d) The four VSP S-wave components X'X', X'Y', Y'X', Y'Y' after the Alford rotation of

60o.


Figure 4.5: The four VSP S-wave components X'X', X'Y', Y'X', Y'Y' received at level #61 (depth

5000.3 ft) after a rotation of 20o to 40o angle, with a step of 1o. The similarity in the rotation

results shows that we cannot have a resolution higher than 10o. The four leftmost traces are the

shear-wave data before the Alford rotation. They are displayed as a reference.


After the optimum rotation of 30o, the traveltime lag ST∆ between the fast and

slow shear-wave components, X'X' and Y'Y', can be estimated at each depth. If we

assume an even distribution of crack density along the whole depth range, the

traveltime lag should increase linearly with depth. The picks of the traveltime lag and

a least-squares fitting line through them are shown in Figure 4.6. The traveltime

lag ST∆ increases by 9 ms from 2000 ft to 11500 ft. The total traveltime ST through

this depth interval is about 1500 ms. The corresponding percentage of shear-wave

traveltime anisotropy SS TT /∆ is 0.6%. According to Hudson's theory, SS TT /∆ can

be directly related to the crack density e by this equation:

S

S

S

S

TT

TT

MM

e∆

−+=∆−=

σµ

24162

2415

869

(4.1)

where M , µ , and σ are the P- and S-wave moduli, and Poisson's ratio, of the

unfractured rock. The derivation can be found in Section 2.2 of Chapter 2. The depth

interval between 1200 ft and 11500 ft is a mixture of shale and sand. Over this

interval, the average Poisson's ratio based on the log data at the Red Mountain well is

around 0.28. According to Equation (4.1), 0.6% traveltime anisotropy corresponds to

a crack density of 0.005. This is the average crack density over a 10300 ft interval.

Geological observations (May et al., 1996) show that the fractures tend to concentrate

in thin layers, especially low-porosity, high-clay-content layers. If the ratio of the

fractured layer thickness to the total interval thickness is 1:10, the crack density in the

thin fractured layers will be 0.05. Moreover, because the 10,300 ft interval contains

two sets of fractures along N110oE+/-15

o and N70

oE+/-10

o, respectively. The shear-

wave anisotropies with symmetry planes along different directions can partially

cancel out each other. This effect will make the apparent anisotropy smaller.

The geological observations (May et al., 1996) show that the fracture orientation

changes with depth. In order to determine the fracture orientation and intensity in the


Cretaceous reservoir rocks, we must remove the anisotropy effect of the overburden.

This is done with layer-stripping techniques (Winterstein and Meadows, 1991a, b).

Our data quality, however, does not yield conclusive layer-stripping results. Noise

can come from both the seismic measurements and the data processing. For example,

an error in the estimation of downhole geophone orientation using P-wave data will

result in a corresponding error in the Alford rotation. A higher signal-to-noise ratio,

and compass-recorded geophone orientations could improve the quality of fracture

analysis using VSP data. The layer-stripping techniques will be discussed in more

detail in the next section, when it is applied to the multi-component surface shear-

wave data.


Figure 4.6: The traveltime lag between the fast and the slow VSP events. To calculate the traveltime

lag, I cross-correlated the fast and slow shear-wave components X'X' and Y'Y' after a 30-degree

rotation was made. The solid line is the least-squares fitting line of the data. The average

traveltime lag per 1000 feet is 9 ms.


4.3 Surface shear-wave birefringence and 2D fracture-density

mapping

So that the subsurface anisotropy could be detected, multi-component seismic

data were collected along Lines GRI-1 and GRI-4 at the Fort Fetterman site. This

collection is sponsored by Gas Research Institute and the Department of Energy. The

base map is shown in Figure 3.1 in Chapter 3.

The standard seismic processing was done at ARCO. I summarize the procedures

below:

1. Inline Geometry Header Load

2. Air Blast Attenuation

3. Apply Refraction Statics

4. True Amplitude Recovery

5. ARCO Fan Filter

6. ARCO Noisy Trace Editing

7. Normal Moveout Correction

8. True Amplitude Recovery (Time-power constant = -1;

spherical spreading 1/(time*vel**2) )

9. CDP/Ensemble Stack

10. F-X Decon (Wiener Levinson filter, 4-40 Hz)

The results are four-component, post-stack S-wave data in the XY coordinates. X

represents the east-west inline direction, and Y the north-south cross-line direction.

In order to find the fracture direction and the amount of shear-wave traveltime

anisotropy, I conducted the following processes:

11. the Alford Rotation

12. Cross-correlation, to pick traveltime lag


13. Layer-stripping techniques, to remove the effects of the overburden anisotropy

above the reservoir level

14. Fracture-density estimation

These procedures are discussed in more detail below.

Figure 4.7 shows the four components of the shear-wave data along Line GRI-4.

The first letter of the four components XX, XY, YX, and YY represents the direction

of the source polarization, and the second letter the receiver polarization. As shown

in Figure 4.7, the significant energy level in the cross traces XY and YX indicates the

presence of subsurface anisotropy. The cross talk will be minimized if the

coordinates are rotated to the symmetry-plane directions of the natural anisotropy.

I applied the Alford Rotation at every 5o increment. The optimum rotation that

minimizes the cross-talk components is a +15o rotation to the X'Y' coordinates, where

the X'-axis is along the N105oE direction. Figure 4.8 shows the GRI-4 data after they

were rotated by +15o to N105oE. At this angle, the energy in the cross-talk

components X'Y' and Y'X' is minimized. The same events in the X'X' section arrive

earlier than those in the Y'Y' section. This indicates that the fractures are along

N105oE, because shear waves polarized parallel to the fracture plane travels faster

than those polarized in other directions. Within any 10o or less, there is no significant

change in the rotation results. Therefore, I consider the uncertainty in the rotation

angle to be about +/-10o. The inferred fracture direction of N105oE+/-10o agrees with

that inferred from the VSP data, N96oE+/-10o, at the Red Mountain well location. It

is also consistent with the geological observation of the N110oE+/-15o fracture set

that appears in the Tertiary and locally in the Cretaceous formations (May et al.,

1996).


Figure 4.7: The four components of shear wave along Line GRI-4. From left to right: XX, XY, YX,

YY. The significant energy level on the mismatched traces XY and YX indicates the subsurface

anisotropy.


Figure 4.8: GRI-4 after 15o Alford rotation to N105oE direction. This is the optimum Alford-rotation

angle at which the minimum energy on the X'Y' and Y'X' components is reached.

After rotating the data to the proper coordinates, I used a cross-correlation method

to pick the traveltime lag between the fast and slow arrivals. When two similar

events are cross-correlated, the lag with the maximum cross-correlation value

corresponds to their traveltime difference. The cross-correlation window should not

be too long so that it excludes other events. However, all X'X' events in the

Cretaceous strata arrive more than 50 ms earlier than the Y'Y' events. To make them

be in a short cross-correlation window, I shifted the X'X' sections by a constant time

of 50 ms. A 100-ms window centered at each event was used to get the remaining

traveltime lag. The traveltime lag is the remaining traveltime lag plus the previous 50


ms shift. Figure 4.9 illustrates the result of the cross-correlation at a few CDP

locations.

Figure 4.9: Cross-correlation results for picking the traveltime lag. The measurement error is about +/-

1ms. The 100 ms here corresponds to a 0-ms shift.

Knowing the uncertainty in picking the traveltime lag is important for judging the

quality of the fracture interpretation. Because of the previous filtering of 4-40 Hz in

processing Step 10, the smallest period is 25 ms. Half of the period is about 12 ms.

A 10% error in picking the highest cross-correlation value corresponds to an error of

about +/- 1ms.

Figure 4.10 shows the traveltime lags for the tops of the Parkman, Sussex, and

Niobrara formations, and the bottom of the first Frontier sand. These lags are the

cumulative lags of all the anisotropy above the reflectors. The difference in lag

between two reflectors is related to the amount of anisotropy between the two events.

Figure 4.11 shows the change in traveltime lag ST∆ in the Parkman, Sussex, Niobrara

formations, and the first Frontier sand. Because the reflection at the top of the

Niobrara formation is weak compared to that from other strong reflectors, its

traveltime-picking tends to have large uncertainty. Figure 4.12 shows the amount of


shear-wave traveltime anisotropy SS TT /∆ in the various intervals. The negative

shear-wave anistropy for the Niobrara and Frontier formations shows that N105oE is

not the fast direction, and the fracture plane is not in the N105oE+/-10o direction in

this interval. To recover the fracture information at the Niobrara-Frontier reservoir

level, layer-stripping analysis (Winterstein and Meadow, 1991a, b) to remove the

overburden effect is required.

30

40

50

60

70

80

90

2150 2200 2250 2300 2350

at Parkman Top

at Sussex Topat Niobrara Top

at 1st Frontier Bottom

She

ar W

ave

Trav

eltim

e di

ffer

ence

(ms)

CDP

S-wave Traveltime Difference along GRI-4

Figure 4.10: Shear-wave traveltime lag along Line GRI-4. The traveltime difference is obtained with a

cross-correlation of the fast (X'X') and slow (Y'Y') events.


-30

-20

-10

0

10

20

30

40

50

2150 2200 2250 2300 2350

Parkman

Sussex

Niobrara and 1st Frontier

She

ar W

ave

Trav

eltim

e di

ffer

ence

(ms)

CDP

S-wave Traveltime Difference in Each Formation along GRI-4

Figure 4.11: Shear-wave traveltime lag generated within each formation along Line GRI-4. The

results are the difference between traveltime differences at the corresponding events as shown in

the previous figure.

-15

-10

-5

0

5

10

15

2150 2200 2250 2300 2350

SussexParkman

Niobrara and 1st Frontier

S-w

ave

Trav

eltim

e A

niso

trop

y (%

)

S-wave Birefringence along GRI-4

CDP

Figure 4.12: The shear-wave traveltime anisotropy in each formation along Line GRI-4.


The first step of layer-stripping analysis is to remove the traveltime lag at the

depth level at which the fracture orientation changes across the boundary. This step

is equivalent to moving the source-receiver system to this depth level. Winterstein

and Meadows (1991a, b) point out that an improper traveltime stripping can cause a

subsequent rotation error. At the top of the Niobrara formation, the signal-to-noise

ratio is low, and picking of the traveltime lag is likely to be contaminated. On the

other hand, the top of the Sussex sand is a strong reflector. Without knowledge of the

exact depth level at which the fracture orientation changes, I attempt to do layer

stripping at both depth levels, and subsequently apply the Alford rotation to find the

optimum fracture orientation at the reservoir depth. Layer stripping at the Niobrara

top and subsequent rotation indicates a N40oE fracture orientation in the Niobrara and

the first Frontier sand. This is inconsistent with the geological observation, and could

be an aritfact of the low signal-to-noise ratio. The removal of the traveltime lag at

the top of the Sussex sand and subsequent rotation, however, yields a optimum

fracture direction of N75oE in the Sussex-Niobrara-Frontier interval. The rotated

shear-wave data rotated to N75oE and N65oE direction are shown in Figures 4.13a

and 4.13b. It is worth mentioning that at the current signal-to-noise ratio, it is

difficult to determine accurately which rotation angle gives smaller cross-talk energy.

However, the rotation to the true symmetry plane of the fractured rock should also

give the largest traveltime lag ST∆ between the fast and slow components. Figure

4.14 shows the amount of traveltime lag along GRI-4. A rotation to N75oE shows a

larger traveltime lag than that of N65oE. Therefore, I chose N75oE to be the fracture

orientation at the Sussex-Niobrara-Frontier interval. This is also consistent with the

geological observations of the fracture set at N70oE+/-10o direction. Assuming that

the anisotropy in the Sussex sand can be ignored, and that the traveltime lag between

the top of the Sussex and the bottom of the first Frontier sand is completely due to the

fractures in the Niobrara and Frontier formations, we can calculate the corresponding

traveltime anisotropy SS TT /∆ , as shown in Figure 4.15. The average crack density in

the Niobrara-Frontier interval can then be estimated with equation (4.1). The result is


shown in Figure 4.16. The CDP range marked by "xline #205" corresponds to a 3D

superbin position. Data within this superbin will be analyzed in detail in the 3D P-

wave analysis. Within this zone, the average crack density is about 0.012. The

measurement error of +/- 1ms will correspond to +/- 0.004 error in the crack-density

estimation. Because the fractures might not be evenly distributed throughout the

Niobrara and Frontier formations, but concentrated in some thin layers, 0.012+/-0.004

is only an average crack density over the Niobrara-Frontier interval. The true crack

density within thin layers can be much higher. Section 3.9 shows that, in the dipole

sonic log data along the Red Mountain well, the shear-wave splitting concentrates in

low-clay-content, low-porosity thin layers. A rough estimate of the the thickness of

the fractured layers is about 12% of the Niobrara-Frontier interval. If this applies to

the CDP locations along GRI-4, the crack density in these layers is about 0.1+/-0.03.

Figure 4.13: (a) Results of layer stripping at the top of the Sussex sand, and the subsequent Alford

rotation to N75oE. Note that the trough near 0 ms is the top of the Sussex sand, and the strong

trough near 600 ms is the bottom of the first Frontier sand.


Figure 4.13: (b) Results of layer stripping at the top of the Sussex sand, and the subsequent Alford

rotation to N65oE. Note that the trough near 0 ms is the top of the Sussex sand, and the strong

trough near 600 ms is the bottom of the first Frontier sand.

-10

-5

0

5

10

2150 2200 2250 2300 2350

S-wave Birefringence along GRI-4 after Re-rotate toN75E (solid line) and N65E (dashed line)

CDP

xline #205

She

ar W

ave

Trav

eltim

e di

ffer

ence

(ms)

Figure 4.14: The traveltime lag between the fast and slow events from the top of the Sussex formation

to the bottom of the first Frontier formation.


-8

-6

-4

-2

0

2

4

6

8

2150 2200 2250 2300 2350

S-w

ave

Trav

eltim

e A

niso

trop

y (%

)

CDP

xline #205

Figure 4.15: The traveltime anisotropy in the Niobrara and Frontier formations, made with the

assumption that the traveltime lag shown in Figure 4.14 is completely attributed to the fractures in

the Niobrara and Frontier formations, but not the Sussex formation.


-0.08

-0.06

-0.04

-0.02

0

0.02

0.04

0.06

0.08

2150 2200 2250 2300 2350

Crack Density in Niobrara and 1st Frontier along GRI-4

Cra

ck D

ensi

ty

CDP

xline #205

Figure 4.16: The crack density in the Niobrara and the first Frontier sand. This is derived from the

shear-wave traveltime anisotropy after layer stripping at the top of the Sussex sand has been done

and the data are re-rotated to N75oE.

Figure 4.17 shows the four components of shear waves along Line GRI-1. The

Alford rotation was applied at every 15o. Figures 4.18 and 4.19 show the results after

rotations of +15o to N105oE, and -15o to N75oE. The CDP range between CDP 2069

and CDP 2350 falls in the 3D P-wave survey area. The Alford rotation shows that in

the south half of the line from CDP 2069 to CDP 2227, the preferred fracture

direction is N105oE+/-15o; in the north half of the line from CDP 2228 to CDP 2350,

the preferred fracture direction is N75oE+/-15o. The transition from N105oE to

N75oE occurs gradually between CDP 2200 and CDP 2260. At CDP 2213 where the

Red Mountain well is located, the inferred fracture direction is N105oE+/-10o. This

finding is consistent with the N96oE+/-10o direction inferred from the VSP data

N96oE+/-10o. The anomalous transition zone of the fracture orientation change

correlates with the change in dip of the bedding planes. The structural features of the

site are given in detail in the appendix.


XX XY YX YY

Figure 4.17: The four components of shear wave along Line GRI-1. From left to right: XX, XY, YX,

YY. The significant energy level on the mismatched traces XY and YX indicates the subsurface

anisotropy.


X'X' X'Y' Y'X' Y'Y'

Figure 4.18: GRI-1 after 15o Alford rotation to N105oE direction. This is the optimum Alford-rotation

angle between CDP 2069 and CDP 2227 at which the minimum energy on X'Y' and Y'X'

components is reached.


X'X' X'Y' Y'X' Y'Y'

Figure 4.19: GRI-1 after -15o Alford rotation to N75oE direction. This is the optimum Alford-rotation

angle between CDP 2228 and CDP 2350 at which the minimum energy on X'Y' and Y'X'

components is reached.

Along Line GRI-1, the traveltime differences between the fast and slow

propagations were picked at several strong seismic events: the Tertiary-Cretaceous

(K-T) boundary, the top of the Sussex formation, and the bottom of the first Frontier

sand. The results are shown in Figure 4.20. Further layer-stripping analysis to

determine the Cretaceous fracture direction was not conclusive because of the low

signal-to-noise ratio along line GRI-1.


0

20

40

60

80

100

2160 2200 2240 2280 2320

Rotate to N105E Rotate to N75E

S-wave Birefringence along GRI-1

CDP

She

ar W

ave

Trav

eltim

e di

ffer

ence

(ms)

at Sussex Top

at 1st Frontier Bottom

at K-T Boundary

Figure 4.20: Shear-wave traveltime difference along Line GRI-1. The traveltime difference is obtained

by cross-correlation of the fast (X'X') and slow (Y'Y') events. Only a few strong events are

picked because of the low data quality.

For later comparison with the analysis of P-wave data, Figure 4.21 shows a

mapping of the fracture direction at the reservoir level in the 3D P-wave superbin

grid. This mapping is made based on surface shear-wave analysis.


Figure 4.21: The fracture directions inferred from the 2D shear-wave data. The directions are shown in

the 3D P-wave superbin grid.

4.4 3D P-wave Velocity Anisotropy and 3D Fracture Network

As discussed in Section 2.3, P-wave velocity varies with propagation direction in

an anisotropic media. When parallel vertical fractures are the source of anisotropy,

far-offset P-wave data will have azimuth-dependent velocity. P-waves travelling in

the fracture plane will have a faster velocity than those traveling in a plane

perpendicular to the fractures. This section analyzes the P-wave traveltime

anisotropy at the Fort Fetterman site, and interprets it in terms of fractures.

As a reference, the P-wave processing procedures are listed below:


1. Inline Geometry Header Load

2. Air Blast Attenuation

3. Apply Refraction Statics

4. Ensemble Balance

5. ARCO Noisy Trace Editing

6. Bandpass Filtering (Ormsby bandpass, zero phase, 4-8-80-88 Hz)

7. True Amplitude Recovery (Time-power constant = 1)

8. ARCO 3D Fan Filter

9. Surface Consistent Decon

10. Apply Residual Statics

11. Trace Equalization (Basis for scaling: mean)

12. ARCO 3-D Coherency Statics

13. Normal Moveout Correction

14. True Amplitude Recovery (Time-power constant = -1;

spherical spreading 1/(time*vel**2) )

15. Bandpass Filter (Ormsby bandpass, zero phase, 10-15-45-60 Hz)

16. Emsemble Reorder (CDP superbin size: 800 ft x 800 ft

Azimuth bin size: 10o; Offset bin size: 500 ft)

17. Ensemble Stack/Combine (partial stack over 10-degree-azimuth 500-ft-offset

bins)

18. Ensemble Stack/Combine (near-offset range: 1k to 3k ft; far-offset range: 5k to 8k

ft)

19. Cross-Correlation, to pick traveltime

20. Sequence Attribute Analysis, to pick peak/trough amplitudes

Steps 1 to 14 were conducted at ARCO. These processes are primarily aimed at

removing noise and statics, and preserving the signal. In Step 15, I applied an

Ormsby bandpass filter of 10-15-45-60 Hz in order to further remove the low


frequency noise below 10 Hz. The original CDP bin size was 80 ft by 80 ft. In each

CDP bin, there is only partial azimuth coverage. In order to improve the azimuth

coverage in each CDP bin, the data was reordered into superbins of size 800 ft by 800

ft. A partial stacking was conducted for each CDP superbin. The traces in each CDP

superbin are binned into eighteen 10o azimuthal bins centered at 5o to 175o azimuths.

Within each azimuthal bin, the traces are binned into 500-ft-offset bins. Traces

within each 500-ft-offset bin are corrected for the normal moveout and stacked. The

velocity used for the NMO correction does not vary with azimuth. Therefore, the

azimuthal variations of the traveltime/velocity are preserved in the partially stacked

traces. Figure 4.22 shows the partially stacked data for the N45oE azimuth. Finally,

the near-offset stack (1000 ft to 3000 ft) and the far-offset stack (5000 ft to 8000 ft)

were generated. Because the data have been partially stacked, each 500-ft-offset bin

will contribute one and only one trace to the final near- and far-offset stacks. The

partial stacking helps to reduce the offset bias for far-offset and near-offset stacking.

Figure 4.23 shows the far-offset stacked traces along 5o to 175o azimuths at the

superbin centered at inline #135 and cross-line #205. In order to get an accurate P-

wave traveltime variation with azimuth, I cross-correlated each trace with the trace at

a perpendicular azimuth. The cross-correlation results for a few CDP's in the 3D

cube are shown in Figure 4.24. Because of the previous filtering of 10-60 Hz in Step

10, the smallest period is 17 ms. Half of the period is about 9 ms. A 10% error in

picking the highest cross-correlation values corresponds to a traveltime picking error

about +/- 1ms. The picked traveltime variation between the top of the Sussex

formation and the bottom of the first Frontier sand at the superbin at inline #135 and

cross-line #205 is shown in Figure 4.25. An error bar of +/- 1ms is shown at each

picks.


Figure 4.22: Partially stacked CDP superbin gathers along azimuth N45oE, i.e., the azimuth bin that

ranges from N40oE to N50oE. The NMO-corrected data are stacked over each 500-ft-offset bin.


Figure 4.23: P-wave 5000ft-to-8000ft far-offset stack at the superbin at inline #135 and xline #205.

The azimuth ranges from 5o to 175 o, with a step of 10 o .


Figure 4.24: Cross-correlation results of P-wave traces along 5 o and 95 o azimuths. The measurement

error is about +/- 1ms.


Figure 4.25: P-wave traveltime between the top of Sussex and the bottom of the first Frontier sand

along various azimuths. This is the relative traveltime obtained by cross-correlation. Traveltime 0

represents traveltime 270ms. Gray lines are the cosine-curve least-squares fits, taking into account

the measurement error of +/- 1ms.

Based on Hudson's theory, the P-wave velocity in fractured media can be

interpreted in terms of the Hudson crack density as:

( ) ( )θφµλµλ 2213 sincos

242

++≈∆≈∆

eUU

TT

VV

P

P

P

P (4.2)

where e is the crack density. The definitions of U1 and U3 in terms of fluid bulk

modulus flK and the crack aspect ratio α , and the derivation of this formula, can be


found in Sections 2.2 and 2.3 of Chapter 2. At a fixed incidence angle, the P-wave

traveltime anisotropy is a cosine function of the azimuth.

Theoretically, three data points along three different azimuths can fully determine

a cosine curve. Because the seismic data contain noise, redundancy in seismic data

can help to improve the cosine estimation and reduce the uncertainty where the data

are noisy. The amplitude data along 18 different azimuths ranging from 5o to 175o,

with a step of 10o are picked except for those extremely noisy traces. Least-squares

fitting of a cosine curve is used to pick the optimum values of fastest P-wave azimuth

angle and variation magnitude. Since data have redundancy, the standard deviation of

the least-squares cosine-curve parameters should be smaller than that of the

measurements. I applied a "bootstrap" method (Davison, 1997) to estimate the

uncertainty in the inferred cosine-curve parameters. The idea is that our

measurements at 18 different azimuths can be treated as 18 random samples out of

infinite number of measurements we could have made. Every time we randomly

draw a group of n data points from the data pool, and fit a least-square cosine curve

through the data, we get an estimation of the true model. This procedure is repeated

many times (in my case, 200 times for each CDP superbin). The outcome is the

distribution of the expected model, i.e., the least-squares cosine fits that are related to

the fracture density and properties. Furthermore, I include the measurement error in

the model estimation: I let each selected measurement have a +/- 1-ms uncertainty.

Before the least-squares estimation is done, the uncertainty will be generated from a

normal distribution with 0 mean and of 1-ms standard deviation, and added to the

data. The gray lines in Figure 4.25 are the least-squares-fitting cosine curves of the

data within CDP superbin centered at inline #135 and cross-line #205. The fitting

was conducted 200 times for each superbin. To test that 200 runs are enough to

generate the proper distribution of the cosine parameters, I randomly generated

several different 200 runs for the same CDP superbin. The estimated mean values of

the cosine parameters from any random 200 runs are within 10% of the standard

deviation. Therefore, 200 runs are enough to give a proper distribution of the cosine


estimations. I calculate the mean and standard deviation of the fast P-wave azimuth

and the magnitude of azimuthal variation.

The distribution of the fast P-wave azimuth and the magnitude of the traveltime

azimuthal variation are shown in Figures 4.26 and 4.27, respectively. These

distributions have taken into account the measurement error, the redundancy of the

data, and the data variation caused by noise. The data display an average fracture

orientation of azimuth 51o, i.e., N39 oE, and an average traveltime anisotropy of 1.6%.

The standard deviation of the estimated fracture orientation is 8 o.

Figure 4.28 shows the estimated fast P-wave direction in the 3D map view, for the

interval between the top of the Sussex sand and the bottom of the first Frontier sand.

Surprisingly, it shows a clustered pattern of N45oE and N60oE. This result does not

agree with either the geological observation, nor the shear-wave splitting results, even

within the standard deviation +/- 8 o range.

Figure 4.26: Histogram of the fast P-wave direction, i.e., fracture orientation, at the superbin at inline

#135 and xline #205. The histogram is based on the 200 cosine fits as shown by the gray lines in

Figure 4.25.


Figure 4.27: Histogram of the P-wave traveltime azimuthal variation from the top of Sussex to the

bottom of the first Frontier sand at the superbin at inline #135 and xline #205. The histogram is

based on the 200 cosine fits as shown by the gray lines in Figure 4.25.


Figure 4.28: Mean value (black solid lines) and standard deviation ( gray lines) of the fast P-wave

direction.

The anomaly can be caused by psuedo-azimuthal variation induced by

heterogeneity or dipping reflectors. Because the P-waves propagate along different

azimuths, they can pick up heterogeneities along the path, and generate an azimuthal

variation in traveltime that is not related to fractures or anisotropy. The ray path

changes with the dip of the reflector, as shown in Figure 4.29. Dipping reflectors can

induce azimuthal traveltime anisotropy. Using the geometry of the travelpath, I

estimated that the traveltime anisotropy as a function of the dip angle, as shown in

Figure 4.30. For a dipping bed of 5o is about 0.5%, and for a dipping bed of 10 o is

about 1.5%. In Figure 4.31, I plot the isopach map with the inferred fracture


directions from P-wave traveltime anisotropy. The isopach map shows the contours

of the depth difference between the top of the Sussex and the bottom of the first

Frontier sand. The gradient of the isopach map is the relative dip of the bottom of the

first Frontier sand relative to the top of the Sussex sand. Only fracture orientations

with less than 20o uncertainty are plotted. At many places, the fracture orientation is

perpendicular to the isopath dip direction, i.e., parallel to the relative dip direction.

The relative dip varies from 0o to 10o. This observation suggests that the P-wave

velocity anisotropy is not a good indicator of fractures when the relative dip of the

bedding is above 5 o.

Figure 4.29: The diagram of P-wave reflected at a dipping bed with a dip angle θ.

Figure 4.30: Dip-induced apparent traveltime anisotropy as a function of the dip angle of the reflector.


Figure 4.31: Fracture orientations inferred from P-wave traveltime anisotropy overlapped by the

isopach map. Only fracture orientations whose standard deviations are less than 20o are drawn

here. The length of the fracture-orientation vector is proportional to the crack density in this map.

Using equation 4.2, I modeled the P-wave traveltime anisotropy for the Niobrara-

Frontier interval. I used the crack density of 0.012, as estimated from the shear-wave

data. I chose the large range of crack aspect ratios from 0.0001 to 0.1. The results

are shown in Figure 4.32, and for both gas and water under high- and low-frequency

conditions. At the CDP superbin at inline #135 and xline #205, a 1.6% anisotropy in

P-wave traveltime is observed. Comparing Figure 4.32 with the observed 1.6%

anisotropy, we notice that the 1.6% is higher than the modeled anisotropy for both gas

and water. Since gas tends to generate larger P-wave velocity anisotropy than stiffer

fluids, the fluid inside the fractures is likely to be gas. However, as we discussed


previously, the P-wave velocity/traveltime data are heavily contaminted by the effect

of dip, and hence are not reliable for fracture characterization.

Figure 4.32: Predicted Vp anisotropy for the Niobrara and Frontier formations, containing parallel

fractures with crack density 0.012, aspect ratio from 0.0001 to 0.1, and various types of crack-

filling fluid.

4.5 P-wave amplitude anisotropy and fracture properties

Section 2.4 shows, theoretically, that aligned vertical fractures can induce

azimuthal anisotropy into the P-wave amplitude. Conventional AVO analysis

averages over the whole azimuth range, and evaluates the amplitude variation with

offset. When the subsurface rock is azimuthally anisotropic, the amplitude varies

with azimuth. Section 2.4 in Chapter 2 shows that at a fixed small incidence angle

(<30o), the P-wave amplitude variation with azimuth is approximately a cosine

function of the azimuth. The variation magnitude is related to the crack density e ,


fluid bulk modulus flK , and the crack aspect ratio α . P-wave amplitude gives us the

possibility of detecting the fracture density and fracture properties.

Using the "Sequence Attribute Analysis" package in ProMAX, I picked the

maximum amplitudes at the bottom of the Frontier formation. Theoretically, at zero

offset, the reflectivity is the same along all azimuths. To ensure this property, the far-

offset amplitudes are normalized by the near-offset amplitudes of the same azimuth.

Figure 4.33 shows the normalized far-offset amplitude variation at the CDP superbin

at inline #135 and crossline #205. Each data point has an estimated error bar of 10%

of the maximum amplitude of +/- 0.1. This accounts for the measurement error.

A bootstrap method was again applied to get the least-squares cosine curves fit to

the data. The measurement error of +/-0.1 (10% of the maximum amplitude) was

taken into account. I consider that each data point corresponds to a normal

distribution with a mean equal to the measured value and a standard deviation equal

to the measurement error of 0.l. The methodology was described in detail in the

previous section. These curves fit to the amplitudes are shown by the gray lines in

Figure 4.33. For each CDP superbin, the bootstrap method repeatedly calculates the

cosine-function parameters 200 times. The distribution of the angle corresponding to

the trough of the cosine curve and the distribution of the ratio of the amplitude

variation to the average amplitude, are shown in Figures 4.34 and 4.35.


Figure 4.33: The amplitude variation with azimuth at the superbin at inline #135 and xline #205. Gray

lines are the cosine-curve least-squares fits, taking into account the measurement error of 10% of

the maximum amplitude.

Figure 4.34: Histogram of the observed fracture orientations based on the P-wave amplitude variation

with azimuth. The azimuth corresponds to the cosine-curve trough (the minimum amplitude) is the

the fracture orientation. The histogram is based on the 200 cosine fits shown by the gray lines in

Figure 4.33.


Figure 4.35: Histogram of the estimated azimuthal variation in P-wave amplitude shown in percentage.

The histogram is based on the 200 least-squares cosine fits shown by the gray lines in Figure 4.33.

To interpret the amplitude azimuthal variation in terms of fracture density and

properties, I calculate the reflectivity at the bottom of the first Frontier sand. The

elastic moduli of the unfracture rocks are taken from the blocked well-log data as

shown in Figure 4.36. Hudson's model was used to calculate the fractured rock

moduli when the rock contains vertical parallel fractures. I considered two crack

densities: 0.012, as measured from the 2D shear waves; and 0.1, as an upper bound.

The far-offset stack has an average incidence angle of 30o. The theoretical curves of

the amplitude azimuthal variation induced by parallel cracks with a crack density of

0.1 are plotted in Figure 4.37. The modeling results indicate that the P-wave

reflectivity has a smaller absolute value along the fracture orientation than

perpendicular to the fracture orientation. Therefore, the trough of the cosine curve

corresponds to the fracture orientation. It has a mean of 3.2o, i.e., N87oE, and a

standard deviation of 18o. This direction is consistent with the geological observation

within the standard deviation. The mean azimuthal variation is 62% normalized by

the average amplitude. Its standard deviation is around 18%.


Figure 4.36: The blocked log data used in the modeling as the properties of the unfractured rocks.

Figure 4.37: The reflectivity at the bottom of the fractured first Frontier sand that contains parallel

vertical fractures with a crack density 0.1.


In order to estimate the fracture physical properties, I compare the variation with

the modeling results for crack aspect ratios of 0.000001 to 0.1, and for gas-filled and

water-filled cracks. The modeling results shown in Figure 4.38 are for crack density

0.012, and those in Figure 4.39 are for crack density 0.1. The current resolution of

the P-wave amplitude variation does not allow us to distinguish the fluid content

within the fractures. The amount of amplitude anisotropy induced by the gas-

saturated and the water-saturated fractures are close, and both agree with the data

within the error range. The data show an amplitude azimuthal variation of 62%. This

is larger than the modeling result. The difference between the data and the model

could be caused by the anisotropic attenuation in the overburden, the focusing effects

of waves traveling in the anisotropic medium, or heterogeity along the wave path.

Figure 4.38: The reflectivity azimuthal anisotropy at the bottom of the fractured first Frontier sand that

contains parallel vertical fractures with a crack density 0.012.


Figure 4.39: The reflectivity azimuthal anisotropy at the bottom of the fractured first Frontier sand that

contains parallel vertical fractures with a crack density 0.1.

Figure 4.40 shows the crack orientation with the standard distribution inferred

from the P-wave amplitude azimuthal variation throughout all bins in the 3D survey

area. Figure 4.41 shows the fracture orientation in the 3D-superbin grid. The length

of fracture-direction vector is proportional to the magnitude of the amplitude

variation. Only those orientations with a standard deviation less than 20o are shown.

At the superbins in which the standard deviations are very large, P-wave amplitude

variation does not give a reliable fracture orientation. The seismically inferred

fracture orientation based on P-wave amplitude roughly agrees with the geological

observations and the fracture orientations inferred from shear-wave data at the

overlapping superbins.


Figure 4.40: The crack orientations derived from the 3D P-wave amplitude azimuthal variation. The

solid lines are the mean value of the fracture orientation. The gray lines are the mean values

plus/minus the standard deviations. This plot highlights the fracture orientations with small

standard deviations: I made the length of the vectors inversely proportional to the standard

deviation of the fracture directions.


Figure 4.41: The crack orientations derived from the 3D P-wave amplitude azimuthal variation. The

length of the vectors is proportional to the crack density in this map. Only fracture orientations

that have a standard deviation of less than 20o are plotted.

4.6 Conclusions

I applied and tested the methodology of using 3D single-component P-wave data

combined with shear-wave data and log data to determine the fracture orientation,

density, and properties at the Fort Fetterman site. Azimuthal anisotropy has been

observed on the P- and S-wave traveltime/velocity, and the P-wave amplitude. I

interpreted the symmetry-plane directions and the magnitude of the anisotropy in

terms of the subsurface fractures' orientation, density, and physical properties.


Results of the 2D shear-wave data, and P-wave amplitude azimuthal variation give a

consistent fracture orientation of N75oE+/-10o and N87oE+/-18o, respectively, at the

Niobrara-Frontier reservoir level. They are consistent with the geological

observations of N70oE+/-10o within the standard-deviation range. The shear-wave

data, however, gives a much smaller crack density than does the P-wave amplitude

azimuthal variation. At this site, the P-wave traveltime anisotropy is probably

contaminated by the effects of dip, and therefore does not give a reliable indication of

the fracture orientation.

The whole-trace Alford rotation of the VSP and 2D shear-wave data shows fast

shear direction of N96oE+/-10o and N105oE+/-10o, respectively. This angle is

consistent with the geological observation of fracture directions N110oE+/-15o in the

Tertiary formations within the standard deviation of our estimates. Because the

fracture orientation varies with depth, as observed in the outcrops, layer-stripping

techniques are required to recover the fracture information in the deeper Cretaceous

formations. The subsequent rotation of the surface shear-wave data shows a preferred

orientation of N75oE+/-10o in the Niobrara and Frontier formations. This angle is

consistent with the fracture orientations N70oE+/-10o observed in outcrop Frontier

sand and in the Formation MicroScanner images. The quality of the subsequent

Alford rotation of the deeper intervals after layer-stripping depends on accuracy in

traveltime-lag picking at the stripping boundary. Therefore, a high signal-to-noise

ratio at the interface of fracture direction change is critical for S-wave fracture

detection in the deep formations. The VSP data do not have sufficiently good signal-

to-noise ratio at the deeper levels for a meaningful application of layer stripping

shear-wave analysis.

Shear-waves anisotropy are not influenced by the fluid properties inside the

fractures. Therefore shear waves can be used to determine the fracture density

without ambiguity from the unknown fluid type and properties. Along Line GRI-4,

the crack density varies between 0 and 0.02. However, this inferred fracture density

is the average fracture density over the Niobrara-Frontier interval being analyzed. It


has been observed both geologically and in the dipole sonic logs that the fractures do

not distribute evenly over the large intervals, but instead concentrate in thin layers of

tight sand. Therefore, the average crack density inferred from the P- and S-wave

traveltime data can be much less than that inferred from the P-wave amplitude

azimuthal variation at the boundary of the fractured rocks.

The P-wave traveltime anisotropy gives an apparent fracture direction of

N39oE+/-8o. This direction, however, is likely to be caused by the effect of dip. This

is shown by the consistency of the dip direction and the predicted fracture orientation.

If P-wave velocity/traveltime anisotropy is used to determine the fractures in fields,

the dip effect must be small compared to the fracture-induced anisotropy.

The magnitude of the P-wave amplitude anisotropy is related to the crack density

and physical properties, including the crack-filling fluids and the aspect ratio. For the

reflection at the bottom of the first Frontier sand, the minimum-amplitude direction

corresponds to the fracture-plane orientation. The corresponding fracture orientation

is roughly along the east-west direction. At many CDP superbin locations, the

inferred fracture orientation based on azimuthal variation of P-wave amplitude shows

a large standard deviations. This results from a high level of noise in the amplitude

data. Even in the blocks in which the inferred fracture orientation has a less than 20o

standard deviation, there are still a few anomalous directions of N45oE and N45oW.

This effect can be caused by a combination of fracture-induced anisotropic

attenuation effects, wave focusing and defocusing in anisotropic media, and

heterogeity along the travel path. I recommend further work in understanding these

other factors that contribute to the P-wave AVOZ. At this signal-to-noise ratio, we

cannot identify the fluid content in the fractures. But the 3D P-wave AVOZ variation

gives us the possibility of mapping the fracture direction over the 3D survey area.

The results of the theoretical modeling can be used as guidelines for seismic

detection of fractures. In general, the amount of anisotropy in shear-wave splitting,

P-wave velocity, and P-wave amplitude increases with the fracture density. The

amount of shear-wave splitting does not depend on the fluid type and the seismic


frequency range. P-waves are sensitve to the types of the fracture-filling fluids, the

fracture aperture, the rock's Poisson's ratio, and the wave frequency. Crack-filling

fluids with higher bulk moduli can induce lower P-wave velocity variation, but higher

P-wave amplitude variation. When the Poisson's ratio of the unfractured rock is high

and other conditions are the same, the shear-wave traveltime lag is larger, and the P-

wave amplitude azimuthal variation is smaller.

4.7 References

Alford, R. M., 1986, Shear data in the presence of azimuthal anisotropy: Dilley,

Texas, SEG 56th Annual Meeting Expanded Abstracts.

Davison, A. C., 1997, Bootstrap methods and its applications, Cambridge University

Press, 582 p.

Greenhalgh, S.A., Mason, I.M., 1995, Orientation of a downhole triaxial geophone:

Geophysics, 60(4), 1234-1237.

Hardage, B.A., 1984, Vertical seismic profiling, London: Geophysical press.

Knowlton, K.B., Spencer, T. W., 1996, Polarization measurement uncertainty on

three-component VSP: Geophysics, 61(2), 594-599.



basement fractures, ARCO-GRI fractured reservoir project report.

Queen, J.H., Rizer, W.D., 1990, An integrated study of seismic anisotropy and the

natural fracture system at the Conoco borehole test facility, Kay county,

Oklahoma, J. Geophys. Res., 95, 11255-11273.


stress directions at Lost Hills field, Geophysics, 56, 1331-1348.



1364.

146

CHAPTER 5

CAN SEISMIC IMAGING HELP TO QUANTIFY FLUID

FLOW IN FRACTURED ROCKS?

5.1 Abstract

We investigate the type of subsurface fracture information that can be extracted

from seismic shear wave analysis, show how rock physics and geostatistics can be

combined to give realistic interpretations, illustrate the variability (non-uniqueness) in

the interpretations by showing equally probable fracture predictions, and evaluate the

uncertainty in rock physics interpretations by looking at the distributions of some

simple fluid flow simulation results.

In the interpretation of fracture-induced seismic anisotropy, the uncertainties in the

stiffness of the embedding rocks versus that of the fractures, in the number of fracture

sets, in the fracture length distribution, and in the span of fracture orientations can give

rise to ambiguity in fracture interpretation. We examine the impact of these

uncertainties on fluid flow responses, and suggest additional information, beyond

seismic, that can increase reliability of fluid flow predictions in fractured formations.

Our results show that seismic analysis can help to constrain predictions of the

spatial distribution of fracture densities, which, in turn, have a very important impact

on fluid flow responses. However, the inference of fracture densities from shear wave

splitting analysis can be unreliable due to uncertainties about some key parameters,

including fracture specific stiffness, fracture orientation, and background lithology

Chapter 5 - Seismic Imaging Helps To Quantify Fluid Flow 147

variations. The uncertainty in fracture orientation distribution does not affect

significantly the final fracture density estimates. The common assumption that

anisotropy is induced by a single set of parallel fractures can lead to misinterpretation

of the fracture density field. In addition, the length and orientation distributions of the

fractures are crucial factors determining connectivity of the fracture system and,

therefore, have an important impact on fluid recovery. The uncertainties can be

reduced by considering additional information about the subsurface fracture system

such as that coming from analog outcrop data, geomechanical studies and production

data. A reliable knowledge of the lithology of the matrix rock is also important.

5.2 Introduction

Seismic methods have been used in fracture detection for more than a decade. The

shear wave splitting techniques (Alford, 1987), among many other techniques, is a

fairly common and robust approach. Its field applications in 2D surface seismic

(Mueller, 1991), 3D seismic (Lewis et al., 1991), dipole sonic log (Mueller, 1994), and

multi-component VSP (Queen and Rizer, 1990, Winterstein and Meadows, 1991a,

1991b) have successfully detected elastic anisotropy and symmetry plane orientations,

which correlate with observed fracture locations and orientations. Fracture detection

using the P-wave velocity (Crampin, 1977) and amplitude (Rueger, 1997; Teng and

Mavko, 1997; Tsvankin, 1997; Lynn et al., 1996), and shear wave amplitude

(Thomsen, 1988; Kendall, 1996) have also been investigated.

The outcome of these seismic methods, however, is strictly speaking, maps of

amount of anisotropy and symmetry plane directions. At best, they have been

interpreted in terms of fracture density and average orientation. They do not lead to

the details of the in situ fracture network distribution that controls the rock

permeability distribution.

To get the subsurface fracture network distribution, we explore how to use the

anisotropy in shear wave splitting data to control the geostatistical reconstruction of

the subsurface fracture networks. We interpreted the shear wave anisotropy in terms


of fracture density and orientation with Schoenberg-Muir's (1989) thin-layer fracture

model. The fracture density mapping was used to guide the stochastic simulation of

the subsurface fracture network. To demonstrate how our approach helped to gather

the hydraulic features of the fracture network, we simulated the fluid flow in the

fracture network. The results show a significant improvement over the pure statistical

approach.

In practice, uncertainty about fracture stiffness, fracture orientation, number of

fracture sets, and unfractured rock matrix properties results in uncertainty in fracture

density predictions. The unknown fracture length distribution also leads to non-unique

realizations of the fracture system. We analyzed the impact of these uncertainties on

fluid flow predictions, and suggests additional information which can help to reduce

these uncertainties.

5.3 Procedures

We begin with an observed image of an in-situ fracture network. The shear wave

velocities are calculated to represent the results of a synthetic seismic shear wave

survey over the site. With the synthetic data, the uncertainties of extracting actual

fracture information from seismic data can be examined without the complication of

field-data noise and measurement errors. We then interpret the shear wave velocities

in terms of fracture density, stochastically simulate the fracture networks that are

consistent with these densities, and perform fluid flow simulation to evaluate the flow

properties of the seismically constrained fracture networks. By comparing the fluid

flow results of the true fracture system with those from simulated fracture networks,

we examine to what extent shear wave survey can help in constraining fluid flow

predictions in fractured reservoirs.


5.3.1 Reference Fracture Image

The reference fracture system is taken from an image (Figure 5.1) of an exposed

outcrop pavement exhibiting two distinct fracture sets. A first set is oriented roughly

along the North-South direction (Set I), and a second is aligned in the East-West

direction (Set II). The horizontal section considered is approximately 136 meters by

52 meters. The fractures were first delineated on the photograph, then scanned and

transformed to pixel format. The resolution necessary to render the fractures visible is

544 by 208 pixels. This is the resolution of the grid on which the fractures will be

simulated. Each pixel represents a 0.25 meter by 0.25 meter square.

Figure 5.1: Reference fracture image digitized from a photograph of an exposed outcrop.

5.3.2 Seismic Modeling and Shear Wave Analysis

Because most fractures in Figure 5.1 are longer than the seismic wavelength, to

calculate the elasticity of the fractured rocks, we chose to use the finely layered model

given by Schoenberg and Muir (1989) rather than the penny-shaped crack models

(Hudson, 1981, 1990; Thomsen, 1993). When a rock block with dimension L contains

N parallel through-cutting fractures perpendicular to the 3-axis (Figure 5.2a), the

rock’s shear stiffnesses can be expressed as:

TEC

+=

144µ

(5.1a)

µ=66C


where µ is the shear stiffness of the unfractured rock, 66C is the rock’s stiffness for

shear wave propagating and polarizing in the fracture plane, 44C is for shear wave

propagating or polarizing perpendicular to the fracture plane, and rE is given by

TT L

NE

κµ= (5.1b)

The fracture shear specific stiffnesses Tκ describes the rate of change of the shear

stress with respect to the fracture’s shear displacement.

1

2 3

32

1

3

1

2

N

E

S

W

(a) (b) (c)

θ

Figure 5.2: (a) Diagram of a set of parallel fractures in Cartesian coordinates; (b) diagram of a set of

fractures uniformly distributed within a angle range in Cartesian coordinates; (c) diagram of two

sets of vertical fractures in Cartesian coordinates. (c) illustrates the orientation of the reference

fractures in a 3D plot.

The shear wave weakly anisotropic parameter γ (Thomsen, 1986) indicates the

amount of shear wave splitting, and can be expressed as a function of fast ( fastSV − ) and

slow ( slowSV − ) shear wave velocities:

slowS

slowSfastST

VVVE

CCC

−

−− −≈=−=

22 44

4466γ (5.2)


where

ρ

ρ

/

/

44

66

CV

CV

slowS

fastS

=

=

−

− (5.3)

ρ is the bulk density of the rock.

When multiple sets of fractures are present in a rock, their impact can be

approximated by a linear summation of compliances of each set. One scenario is that

fractures are uniformly distributed within an angle range θ as shown in Figure 5.2b.

By integrating the fracture-induced compliance change, we get the corresponding

elasticity of a fractured rock as:

CET

55

112 2

=+ +

µθ

θsin

(5.4)

CET

44

112 2

=+ −

µθ

θsin

Note that as θ approaches zero, the shear wave moduli approach the parallel fracture

limit given by equation (5.1). Figure 5.2c illustrates the 3D image of the fracture

system as previously shown in Figure 5.1. In this coordinate system we can express

the shear wave moduli as:

CE ET T

55

11

12

2

2

112 2

12 2

=+ +

+ −

µθ

θθ

θsin sin

(5.5)

CE ET T

44

11

12

2

2

112 2

12 2

=+ −

+ +

µθ

θθ

θsin sin


where 1θ and 2θ are the angular range of fracture orientations for Set I and Set II, and

1TE and 2TE are given by equation (5.1b) for Set I and Set II, respectively.

We divide the survey area into 8 by 4 blocks. Each block represents a bin or super

bin in a 3D seismic survey. The bin size is 17 meters by 13 meters (68 pixels by 52

pixels). The fracture density and angle distribution of Set I and Set II can then be

counted for each bin. Figure 5.3 shows the fracture density count and angle

distribution derived from Figure 5.1. We model the shear moduli and velocities for

vertically propagating shear waves polarized along the N-S and E-W directions with

equations (5.3) and (5.5), and the corresponding shear anisotropic parameter using

equation (5.2). The fracture specific shear stiffness is chosen to be 25 MPa/mm such

that the calculated shear wave anisotropy over the fracture zone is around 5% to 15%.

The properties of the background unfractured rock are the lab measurements of a low-

porosity and low-permeability sandstone:

P-wave velocity: 4.67 km/s

S-wave velocity: 3.09 km/s

density: 2.53 g/cm3

porosity: 3.5%

permeability: 0.66 mD

Figure 5.4 shows the modeling results of the shear wave moduli, velocities for the

N-S and E-W polarizations, and the anisotropic parameter. We take these as the

"observed" seismic parameters, which we will interpret for fracture distribution.

To infer the fracture density (number of fractures per block), we assume that the

velocity change is induced by two sets of vertical sub-parallel fractures along the N-S

and E-W azimuths respectively, and that the values of the unfractured rock properties

are known. We estimate the fracture density assuming strictly parallel fractures, and

refer to this interpretation as Case 1. Figure 5.5 shows the integer part and the residual

decimal part of the fracture number per block separately, since the stochastic fracture


simulation model considers only an integer number of fractures per block. The integer

part of the density is exactly the same as the true density map as expected. The

decimal part of the fracture number in each block is the result of the parallel fracture

assumption; it is much smaller than the integer part, and can therefore be ignored.

Since in reality, we may not have precise information of fracture orientation and

embedding rock properties, the density estimation can be ambiguous and non-unique.

We will discuss this in more detail later in this paper.

(a)

(b)

(c)

(d)

Figure 5.3: Fracture density maps of the reference fracture image for (a) Set I and (b) Set II; azimuth

spread maps (degrees) for (c) Set I and (d) Set II in each block consisting of 68 by 52 pixels (17m

by 13m).


(a)

(b)

(c)

(d)

(e)

Figure 5.4: Forward modeling results of (a) shear wave moduli (GPa) and (c) velocities (km/s) for

vertical propagating shear wave polarized along the E-W direction, (b) shear wave moduli and (d)

velocities for shear waves polarized along the N-S direction, (e) shear wave anisotropic parameter.


5.3.3 Fracture Network Simulation

An algorithm to stochastically simulate discrete fractures in layered reservoirs has

recently been developed by Gringarten (1997). It is based on geomechanical rules of

fracture propagation and aims to account for various types of information about the

fractures in the subsurface.

The information required by the model to simulate fracture propagation are

fracture density and orientation for each fracture set to be simulated and rules for

timing relations (chronological order of appearance) between the different sets. A

more detailed description of the algorithm can be found in Gringarten (1997).

We simulated the fracture networks based on the seismically-determined fracture

density estimates shown in Figure 5.5. The fracture simulation model, being

stochastic, generates multiple equiprobable realizations of the fracture system. This is

critical, since seismic data can yield fracture density, but rarely image individual

fractures. Figure 5.6 shows four simulated fracture images, all consistent with the

seismically-determined fracture density map given in Figure 5.5. The fractures are

assumed to be vertical, strictly parallel and aligned with the N-S (Set I) and E-W (Set

II) directions. The extent of the fractures is guided by the spatial distribution of the

fracture density. Uncertainty in the maximum extent of the fractures will be discussed

later in the paper.


(a)

(b)

(c)

(d)

Figure 5.5: Fracture density estimation for Case 1 (parallel fracture assumption): (a) integer part for Set

I; (b) integer part for Set II; (c) residual decimal part for Set I; (d) residual decimal part for Set II.


Figure 5.6: Four equiprobable realizations of the fracture system for Case 1 assuming parallel

fractures for both sets.

5.3.4 Fluid Flow Simulation

In order to evaluate the flow characteristics of the fracture systems, we simulated

the single-phase flow through the reference image and the simulated fracture networks

by using the streamline simulation code 3dsl (Batycky et al., 1997). This code differs

from traditional finite-difference flow simulators by decoupling the full 3D problem


into multiple 1D problems along streamlines. The geometry of the streamlines are

defined by the permeability variations and the well conditions. The fluids are moved

along the streamlines rather than through an arbitrarily discretized grid. Streamline

flow simulators are much faster and have been shown to be as or more accurate than

conventional flow simulators in certain situations. The speed enables rapid processing

of multiple alternative high resolution reservoir models. A thorough presentation of

streamline simulation can be found in Batycky et al. (1997) and Thiele (1996).

We will look at tracer flow through the simulated fracture systems. The fluid

injected has identical properties to the one originally in place. The fluids are assumed

incompressible. Therefore, the flow responses will only be affected by variations in

permeability values and not by the fluid properties. Tracer flow is thus well suited to

investigate the effects of permeability heterogeneity.

An injector well was placed on the left edge of the grid, and a producer well at the

right side. Tracer is injected at a constant pressure of 2000 psi. Production is set at

the constant rate of approximately 0.01 pore volume per day. An analytical mapping

of the tracer flow solution along the streamlines was used. The background matrix

rock has a constant porosity of 3.5% and permeability of 0.66 mD. We assumed that

the fractured rock pixels have a constant permeability of 100 mD, and a constant

porosity of 3.5%, similar to the porosity of the matrix to emphasize the effect of

permeability contrast. Figure 5.7 shows an example of the tracer saturation profile

through the reference fractured rock after 0.5 pore volume of tracer has been injected.

The straight front is due to the homogeneity of the matrix.

Two flow responses are considered: recovery of fluid initially in place and

production of injected tracer. Recovery indicates the sweep efficiency through the

fracture network, and tracer-cut response gives an idea of the connectivity of the

fracture network.


Figure 5.7: Tracer saturation profile after breakthrough through the fractured formation containing the

reference fracture network.

Note that the streamline simulator does not account explicitly for any sort of

matrix-fracture interaction. This may be an a-priori drawback of the method when

applied to fractured reservoirs, however, it may be sufficient in some cases to mimic

flow through fractured rocks, particularly if one assumes that changes in the pressure

field are dominated by variations in permeability as is the case here. Further

discussion can be found in Gringarten (1997).

We simulate flow through the reference fracture network shown in Figure 5.1 and

through various simulated fracture networks. Fluctuations are expected from multiple

equiprobable realizations. As an example, we generate 50 equiprobable realizations

similar to the ones shown in Figure 5.6. Flow simulations are performed on all 50

images. The resulting responses are shown in Figure 5.8 along with the flow

responses of the reference image. The true responses fall within the predicted range of

simulated responses. We will consider only a single realization of the fracture

networks for each of the scenarios retained for the uncertainty analysis in the next

section of the paper.

We also compute the effective permeability values in the E-W direction using a

simple single-phase pressure solver, considering a constant pressure difference across

the E-W direction, and no-flow boundaries on the other faces. These effective

permeability will gives us some indication on the global behavior of the fractured

rock. The effective permeability computed for the reference case is 3.2 mD.


Figure 5.8: Recovery and tracer-cut responses for 50 equiprobable simulations (gray lines) along with

the responses of the reference image (black line).

5.4 Uncertainty in Interpretation of Seismic Data for Fractures

To generate the fracture images shown in Figure 5.6, we assumed that we have

some prior knowledge of the fracture specific stiffness, the background rock

properties, the orientation of the fractures, and the maximum extent of the fractures.

In practice, these are poorly known. We investigate how the uncertainty in these

parameters may change the fluid flow responses in the fractured rock by simulating a

fracture network for each uncertainty assumption, and by processing this simulated

network through the flow simulator 3dsl. A complete study should include several

realizations for each case to account for the fluctuations in the stochastic fracture

simulations as done for Figure 5.8. This was not done here to emphasize the impact of

varying certain key parameters. However, each simulation was generated using the

same random seed number.


5.4.1 Unknown Fracture Stiffness

Equation (5.1) shows that the fracture density is inversely proportional to the

fracture specific stiffness. Barton and Bandis (1982) collected the shear stiffness of

rock joints of 650 data points from 35 sources, including those from tilt or push tests,

and those derived from earthquake events reviewed by Nur (1974). The fracture

stiffness ranges from 0.001 MPa/mm to above 100 MPa/mm. Pyrak-Nolte, Myer, and

Cook (1992) used 104 MPa/mm fracture shear stiffness to explain their lab ultrasonic

measurements. These stiffness values cover a tremendous range. Overestimation of

stiffness will cause overestimation of fracture density, and vice versa. We consider the

case where the fracture stiffness is 50 MPa/mm (Case 2). This stiffness is chosen to be

close to the reference case fracture stiffness 25 MPa/mm in order to simulate the

fracture network without changing to a finer grid. Twice the amount of the original

fractures (Figure 5.9a and 5.9b) are necessary to yield the same shear wave velocity

responses (Figure 5.4). A corresponding possible fracture simulation is shown in

Figure 5.9c. An additional parameter, which we have not considered, is that larger

fracture stiffness will probably correlate with lower fracture permeability.

Comparing the flow simulation results for Case 1 and 2 in Figure 5.10, we see that

Case 2 will yield a lower recovery of fluid initially in place, because more injected

fluid is channelized in the fractures and thus less tracer sweeps the matrix. When

producing at a constant rate, Case 2 shows a later breakthrough time than Case 1,

because the same amount of injected tracer is separated through a larger number of

fractures. However, shortly after breakthrough, more tracer appears at the producing

well compared to Case 1, creating a much higher tracer-cut.

The effective permeability of the fractured rock obtained by imposing a constant

pressure drop across the whole domain is as expected, much higher (about twice) for

Case 2 (9.8 mD) than for Case 1 (5 mD), entailing much faster flow through the whole

system.


(a)

(b)

(c)

Figure 5.9: Fracture density maps for Case 2 for (a) Set I and (b) Set II assuming that the fracture

shear specific stiffness is 50 MPa/mm; (c) simulated fracture network based on the density maps

in (a) and (b).

Figure 5.10: Recovery and tracer-cut responses for Case 1 and Case 2.


5.4.2 Unknown Fracture Orientation

In the previous seismic velocity inversion, we assumed parallel fractures. The true

fracture image has small variations of orientation. The variations are not

distinguishable seismically. To evaluate the parallel fracture-assumption, we simulate

the fracture networks by taking the true fracture angle distribution (Figure 5.3c and d)

into account (Case 3). The seismic velocity inversion results using equation (5.5)

yield little variation in density predictions, compare Figures 11a and b with Figures 3a

and b. The simulated fracture image in Figure 5.11c is similar to the true image, and

as could be expected from this visual judgment, the flow results for this image and the

reference are almost the same, see Figure 5.14.

Larger fracture strike angle distribution has been observed at many sites (Mueller,

1991; Lauback, 1992; Lorenz, 1992; Barton and Zoback, 1992). Instead of having a

true angle distribution map, we may also assume that the fractures have a uniform

orientation distribution between -10° and +10° azimuth for Set I, and between +80°

and +110° azimuth for Set II (azimuth 0° is strict North, and the azimuth angle is

measured clockwise). Using equation (5.5), and assuming that both θ1 and θ2 are 20°,

we obtain the fracture density map shown in Figure 5.12. As in Case 1, the residual

decimal part of the fracture density is much smaller than the integer part, and can be

ignored. Comparing the fracture density with that of the true fracture image, we notice

that a small angle distribution 20° will barely affect the density estimation. This can

lead to two types of simulated fracture images if we assume that: 1) the fractures

within a set follow an orientation field and cannot intersect (Case 4), or 2) that the

fractures are perfectly straight, with different orientations, and can intersect each other

(Case 5). The simulated images are shown in Figure 5.13a for Case 4 and in Figure

5.13b for Case 5. This drastic difference in angle distribution as compared to the

reference image has a large impact on fluid flow predictions, see Figure 5.14. For

production at a constant rate, the tortuosity of the fracture system greatly retards tracer

breakthrough. However, it forces a larger sweep of the fluid initially in the matrix as


can be seen on the recovery curve. Surprisingly, there is very little difference between

the responses of Cases 4 and 5, though a later breakthrough can be observed for Case

4, because its fractures are much less connected.

The large variability in fracture orientation is also seen to reduce the effective

permeability of the fractured rock in Case 4 (2.7 mD) and Case 5 (2.7 MD), and even

in the reference case (3.2 mD) where the fracture orientation is less variable than in

Cases 4 and 5, but more than in Case 3 (4.9 mD).

(a)

(b)

(c)

Figure 5.11: Fracture density maps for Case 3 for (a) Set I and (b) Set II by taking the true fracture

angle distribution into account; (c) simulated fracture network based on the density maps in (a)

and (b) and the true fracture angle distribution.


(a)

(b)

(c)

(d)

Figure 5.12: Fracture density maps for Case 4 and 5 assuming 20° angle distribution for (a) integer

part of Set I; (b) integer part of Set II; (c) decimal part of Set I; (d) decimal part of Set II.


(a)

(b)

Figure 5.13: Simulated fracture networks for (a) Case 4 and (b) Case 5.

Figure 5.14: Recovery and tracer-cut responses for Cases 3, 4, and 5.


5.4.3 Unknown Number of Fracture Sets

In shear wave splitting analysis, a common assumption is that the anisotropy in

shear wave velocity is caused by only one set of parallel fractures. While outcrops,

cores, FMS FMI images often show multiple fracture sets (Nelson, 1985; Barton and

Zoback, 1992), practitioners often take the fast shear wave velocity to be that of the

unfractured rock matrix, and map the shear wave splitting amount into fracture density

using equation (5.2). This assumption leads to the fracture density estimations shown

in Figure 5.15a and 5.15b (Case 6). We can see that the fracture density predictions in

the upper part of the grid, where Set II is absent, are the same as the reference density.

But the lower part of the density map gives a much smaller density prediction since the

anisotropy effects of the two fractures sets are perpendicular and partly cancel out.

The subsequent fracture simulation is presented in Figure 5.15c, and the flow

simulation results are shown in Figure 5.16.

Visually, the simulated image is very different from the reference image, and as

could be expected, has a lower effective permeability (2.5 mD as compared to 3.2 mD

for the reference system) due to the lack of connectivity in the image. This also entails

a later breakthrough. A higher recovery can also be observed since more tracer is

pushed through the matrix. The lower tracer-cut of Case 6, as compared to the

reference case, can be explained by the fact that less fractures are connected to the

producing well, yielding a lower influx of tracer.


(a)

(b)

(c)

Figure 5.15: Fracture density maps for Case 6 for (a) Set I and (b) Set II; (c) simulated fracture

network based on the density maps in (a) and (b).

Figure 5.16: Recovery and tracer-cut responses for Case 6.


5.4.4 Unknown Lithologic Variations

Uncertainty in background rock properties can also propagate into the fracture

density estimations. Figure 5.17 shows a set of lab measurements of P- and S-wave

velocities of tight gas sandstone under 40MPa effective pressure (Jizba, 1991). Under

this high pressure, most of the fractures are closed. The velocity variations are due to

the lithology variation. If we do not take the lithology variation into account, but use a

constant unfractured rock velocity, we will overestimate or underestimate the fracture

density. To illustrate this (Case 7), we assume that instead of having a constant

velocity background, the embedding rock velocity shown in Figure 5.18 is spatially

varying. It increases from West to East with small random increments. The total

velocity change is about 20%. We calculate the shear wave moduli and velocities of

the corresponding fractured rock as shown in Figure 5.19. The spatial variation in the

moduli and velocities of the fractured rock is partly due to the embedding rock

velocity variation, and partly to the spatial distribution of the fractures. If, in the

velocity inversion process, we assume the background variation known, the results

will be the same as in Case 1. However, if the background velocity information is

only available in the middle block of the southern edge of the survey area, we have:

P-wave velocity: 4.67 km/s

S-wave velocity: 3.09 km/s

density: 2.53 g/cm3

We can estimate the fracture density by assuming that the background rock over

the whole area has the measured velocities. By comparing the true density maps with

the seismically derived density maps shown in Figure 5.20 under the assumption of

constant background velocity, we can see that we overestimate the fracture density to

the west where the background velocity is lower, and underestimate fracture density to

the east where background velocity is higher. Figure 5.20c shows the simulated

fracture system. However, the flow responses for Case 7 and for the reference image


are very similar, see Figure 5.21. The increase in estimates of fracture densities is not

sufficient to affect the connectivity of the network and therefore barely impacts

recovery and tracer-cut responses. The addition of the connected fractures, however,

increases the effective permeability of the system to 5.6 mD vs. 3.2 mD for the

reference field.

2.4

2.6

2.8

3

3.2

3.4

3.6

3.5 4 4.5 5 5.5 6

Vp (km/s)

Figure 5.17: Lab measurement of P- and S-wave velocities of tight gas sandstone samples under 40

MPa effective pressure. The data are from Jizba (1991).

Figure 5.18: Velocity map (km/s) of the background unfractured rock for Case 7. The velocity spatial

variation in the E-W direction is about 20% with a small random variation along the N-S direction.


(a)

(b)

(c)

(d)

Figure 5.19: The shear wave moduli (GPa) and velocities (km/s) of the fractured formation for Case 7.

(a) shear modulus for E-W polarization; (b) shear modulus for N-W polarization; (c ) shear wave

velocity for E-W polarization; (d) shear wave velocity for N-S polarization.


(a)

(b)

(c)

Figure 5.20: Density maps for Case 7 for (a) Set I and (b) Set II, (c) simulated fracture network based

on the density maps in (a) and (b).

Figure 5.21: Recovery and tracer-cut responses for Case 7.


5.4.5 Unknown Fracture Length

In addition to fracture density, fracture length is another important controlling

factor in stochastic fracture simulation, though it is not a requirement of the fracture

simulation algorithm. We have assumed that the fracture length does not have an

upper or lower bound, but instead that it is guided by the spatial distribution of the

fracture density. Lauback (1992) showed that the outcrop fracture traces can have

various length. If we have reasons to believe that the fractures have a maximum

possible length, the fracture simulation will yield different images. By assuming the

maximum fracture length to be 7.5 meters or 30 pixels (Case 8), 22.5 meters or 90

pixels (Case 9), and 45 meters or180 pixels (Case 10), we generate the fracture images

shown in Figures 22a to 22c.

The shorter fractures of Case 8 do not enable connectivity through the fracture

system. This entails a large sweep of the matrix shown by a high recovery, and a slow

tracer movement through the system shown by a late breakthrough at about 0.4 PVI

(pore volume of tracer injected), see Figure 5.23. In comparison, the longer fractures

of Cases 9 and 10 yield a connectivity similar to the one of the reference system as

shown by similar flow response curves. Slightly later breakthrough, compared to that

of the true response, can be observed and is due to the more tortuous paths taken by

the tracer in the connected fracture network.

The effective permeability of Cases 9 and 10 are similar (4.4 mD and 4.9 mD,

respectively); the one of Case 8 is lower at 2.1 mD.


(a)

(b)

(c)

Figure 5.22: Simulated fracture networks: (a) Case 8 - maximum fracture length is 7.5 m (30 pixels);

(b) Case 9 - maximum fracture length is 22.5 m (90 pixels).; (c ) Case 10 - maximum fracture

length is 45 m (180 pixels).

Figure 5.23: Recovery and tracer-cut responses for Cases 8, 9, and 10.


5.4.6 Multiple Uncertainty Sources

In practice, all of the sources of uncertainty appear simultaneously. We present a

simple example to illustrate the possible complications that can be expected in field

studies.

For example, the fracture length and fracture orientation can simultaneously affect

the behavior of the fracture system. Consider the case where only the fractures of Set

II are present in the rock (Case 11). With the parallel fracture assumption and no

maximum length constraint, we obtain the fracture image shown in Figure 5.24a.

With 20° azimuth spread, and different maximum lengths, 7.5 m (Case 12), 22.5 m

(Case 13), and 45 m (Case 14), we obtain the fracture simulations shown in Figure

5.24b to Figure 5.24d.

The flow responses of Case 11, shown in Figure 5.25, are extremely similar to the

reference. This is due to the fact that a similar number of fractures connect the injector

to the producer. This means that the fractures of Set I are of secondary importance for

this well configuration, and that modeling efforts should focus on the fractures of Set

II. However, if the fractures were shorter, the flow responses would be drastically

different as can also be seen in Figure 5.25.

The effective permeability can also be greatly reduced: 0.9 mD for Case 12, 1.7

mD for Case 13, and 1.9 mD for Case 14, vs. 3.2 mD for the reference network.

5.5 Discussion

Variability in estimated flow responses can be reduced if the simulation of

fractures is well constrained. The simulated fracture networks depend greatly on the

estimation of fracture densities. In turn, variations in fracture density estimates have a

very important impact on fluid flow responses.


(a)

(b)

(c)

(d)

Figure 5.24: Simulated fracture networks:

(a) Case 11 - no length constraint, parallel fractures.

(b) Case 12 - maximum fracture length is 7.5 m; azimuth spread is 20°.

(c) Case 13 - maximum fracture length is 22.5 m; azimuth spread is 20°.

(d) Case 14 - maximum fracture length is 45 m; azimuth spread is 20°.


Figure 5.25: Recovery and tracer-cut responses for Cases 11, 12, 13, and 14.

Seismic analysis can help to constrain predictions of the spatial distribution of

fracture densities. However, the inference of fracture densities from shear wave

splitting analysis can be unreliable due to uncertainties about some key parameters,

including fracture specific stiffness, fracture orientation, and background lithology

variations. Our initial results for the specific production pattern here retained show

that the uncertainty in fracture orientation distribution does not affect significantly the

final fracture density estimates, while other unknowns can be more important in

estimating fracture density. The common assumption that anisotropy is induced by a

single set of parallel fractures can lead to misinterpretation of the fracture density field.

In addition, the length and orientation distribution of the fractures are crucial factors

determining connectivity of the fracture system and have, therefore an important

impact on fluid recovery.

The uncertainty in seismically derived densities, in fracture length, and in fracture

orientation can be reduced by considering additional information about the subsurface

fracture system such as coming from analog outcrop data, geomechanical studies, and

production data. A reliable knowledge of the lithology of the matrix rock is also

important.


5.6 Acknowledgments

This work was supported by Gas Research Institute Contract 5094-210-3235, the

affiliate companies of the Stanford Rock Physics Project and of the Stanford Center

for Reservoir Forecasting.

5.7 References

Alford, R. M., 1987, Shear data in the presence of azimuthal anisotropy; Dilley,

Texas: Geophysics, 52, No. 3, 424.

Barton, C., and Zoback, M., Self-similar distribution and properties of macroscopic

fractures at depth in crystalline rock in the Cajon Pass scientific drill hole, Journal

of Geophys. Res., 97, No. B4, 5181-5200.

Barton, N. and Bandis, S., Effects of block size on shear behavior of jointed rock,

Proceedings - Symposium on Rock Mechanics, 23, 739-760

Batycky, R, 1997, A three-dimensional two-phase field scale streamline simulator,

PhD thesis, Stanford University, Stanford, CA.

Carrera, J., and Neuman, S.P., 1986, Estimation of aquifer parameters under transient

and steady state conditions, Water Resources Research, 22, No. 2, 228.

Carrera, J., and Glorioso, L., 1991, On geostatistical formulations of the groundwater

flow inverse problem, Advances in Water Resources, 14, No. 5, 273-283.

Crampin, S., and Bamford, D., 1977, Inversion of P-wave velocity anisotropy,

Geophys. J R. astr. Soc., 49, 123

Datta-Gupta, A., Vasco, D. W., Long, J.C.S., D’Onfro, P.S., and Rizer, W.D., 1005,

Detailed characterization of a fractured limestone formation by use of stochastic

inverse approaches, SPE Formation Evaluation, Sept., 133-140.

Gringarten, E., 1997, Geometric modeling of fracture networks, Ph.D. thesis.

Jizba, D., 1991, Mechanical and acoustical properties of sandstones and shales, Ph.D.

thesis


Kendall, R., 1996, Shear-wave amplitude anomalies in south-central Wyoming,

Leading Edge, 15, No. 8, 913-920.

Laubach, S., 1992, Fracture networks in selected Cretaceous sandstones of the Green

River and San Juan Basins, Wyoming, New Mexico, and Colorado, Geological

studies relevant to horizontal drilling: examples from western North America,

Rocky Mountain Association of Geologists, 115-127.

Lewis, C., Davis, T., and Vuillermoz, C., 1991, Three-dimensional multicomponent

imaging of reservoir heterogeneity, Silo Field, Wyoming, Geophysics, 56, No. 12,

2048-2056.

Long., J.C.S.,et al., 1991, An inverse approach to the construction of fracture

hydrology models conditioned by geophysical data; an example from the

validation exercises at the Stripa Mine, Intl. J. Rock Mech. Min. Sci. & Geomech.

Abstr. 28, No 2/3, 121.

Lorenz, J., Hill, R., 1992, Measurement and analysis of fractures in core, Geological

studies relevant to horizontal drilling; examples from western North America /

Schmoker, James W., Coalson, Edward B.; Brown, Charles A., 47-59

Lynn, H., Simon, K. M., Bates, R., and Van Dok, R., Azimuthal anisotropy in P-wave

3-D (multiazimuth) data, Leading Edge, 15, No. 8, 923-928.

Mueller, M. C., 1991, Prediction of lateral variability in fracture intensity using

multicomponent shear-wave surface seismic as a precursor to horizontal drilling

in the Austin Chalk, Geophys. J. Int., 107, 409-415.

Mueller, M. C., 1992, Using shear waves to predict lateral variability in vertical

fracture intensity: Geophysics: The Leading Edge of Exploration, 11, No. 2, 29-

35.

Mueller, M. C., 1994, Case studies of the dipole shear anisotropy log, SEG Expanded

Abstract, 64, 1143-1146.

Nelson, R., 1985, Geological analysis of naturally fractured reservoirs

Nur, A., 1971, Effects of stress on velocity anisotropy in rocks with cracks, Journal of

Geophys. Res., 76, No. 5, 1270-1277.


Nur, A., 1974, Tectonophysics: The study of relations between deformation and

forces in the earth, General Report Proc. 3rd Int. Cong. Of Int. Soc. Rock mech.,

Denver, Vol 1A, 243-317.

Pyrak-Nolte, L., Myer, L., Cook, N., 1992, Anisotropy in seismic velocities and

amplitudes from multiple parallel fractures, Journal of Geophys. Res., 95, No. B7,

11345-11358.

Queen, J., and Rizer, W., 1990, An integrated sutdy of seismic anisotropy and the

natural fracture system at the conoco borehole test facility, Kay County,

Oklahoma, Journal of Geophys. Res., 95, No. B7, 11255-11273.

Rueger, A., 1997, P-wave reflection coefficients for transversly isotropic models with

vertical and horizontal axis of symmetry, Geophysics, 62, No. 3, 713.

Schoenberg, M., and Muir, F., 1989, A calculus for finely layered anisotropic media:

Geophysics, 54, No. 5, 581-589.

Teng, L., and Mavko, G., 1997, P-wave reflectivity at the top of fractured sandstone,

SEG expanded abstract, Vol II, 1989

Thiele, M., Batycky, R., Blunt, M., and Orr, F., 1996, Simulating flow in

heterogeneous media using streamtubes and streamlines, SPE RE, 10, No. 1, 5-

12.

Thomsen, L., 1986, Weak elastic anisotropy: Geophysics, 51, No. 10, 1954-1966.

Thomsen, L., 1988, Reflection seismology over azimuthally anisotropic media,

Geophysics, 53, No. 3, 304-313.

Tsang, C.F., Tsang, Tsang, Y.W., and Hale, F.V., 1991, Tracer transport in fractures:

analysis of field data based on a variable-aperture channel model, Water

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stress directions at Lost Hills field, Geophysics, 56, 1331-1348




1364

182

APPENDIX

REVIEWS OF THE GEOLOGICAL FRAMEWORK

OF THE STUDY SITE

The seismic data and log data in this study were collected from the Fort Fetterman

site at the southwestern margin of the Powder River Basin, in Converse County, east-

central Wyoming. To give the readers a general overview of the structural features

and regional stratigraphy of this site, I include a digest of the report "regional

geological framework and site description" (Walters, Chen, and Mavko, 1994) as the

first part of the appendix. The second part reviews the published geological

observations of the fracture existence and attributes at Fort-Fetterman site, southern

Powder River Basin (May et al., 1996), and at Moxa Arch and adjacent Green River

Basin in southwestern Wyoming (Laubach, 1991, 1992a, 1992b; Dutton et al., 1992).

In Chapter 4 "Integrated seismic interpretation of fracture networks", I used the

geological information presented here to justify the rationality of the fractured-rock

models.

A.1 Geological Settings of Fort Fetter Site and Powder River Basin

A.1.1. Structure Features

The Powder River Basin was formed during the Laramide Orogeny that occurred

during latest Cretaceous to early Tertiary time in the western Cordillera (Dickinson et

al., 1988). The typical structural style in the Rocky Mountain Region consists of a

Appendix - Geological Framework 183

series of "basement-cored uplifts and intervening sediment-filled basins" (Dickinson

et al., 1988) over a wide area. The Fort Fetterman site is located at the southwestern

margin of the Powder River Basin, bounded to the south and west by the Casper Arch

to the southeast by the Hartville Uplift (Figure A.1).

Colorado

Wyoming

Big Horn Mountains

Montata

Powder River Basin

Black Hills Uplift

South Dakota

Nebraska

Hartvil

le Upli

ftLaramie Mountains

Wind River Basin

Shirley Basin

Study AreaCasper

Arch

Figure A.1: Structural features in eastern Wyoming, from Mitchell and Rogers (1993), showing

Powder River Basin, and surrounding areas. The study area is marked by a dot.


Mitchell and Rogers (1993) noted that the southern end of the Powder River basin

has been significantly influenced by an extensioinal system of small throw (30 feet or

less), nearly vertical normal faults that affects Lower Cretaceous, Upper Cretaceous,

and Tertiary units. The fault systems appear to trend northwest-southeast in the

south-central part of the basin, and northeast-southwest at the southern margin,

parallel to Hartville Uplift (Figure A.1). Mitchell and Rogers proposed that these

faults are basement derived, and result in significant fracture potential that may

control secondary porosity diagenesis. As the normal faults propagated upward

through the Lower Cretaceous rocks, fractures developed at the erosional/depositional

surface of the Upper Cretaceous Niobrara Formation.

At both the Niobrara and the Frontier levels, the axis of an anticline trends

southwest-northeast through the central portion of the Fort Fetterman site. Figure A.2

and A.3 show the structure contour maps of on the formation tops overlapped by six

2D lines of multi-component seismic surveys, including GRI-1, GRI-4, and four

previous surveys RMC0021 to RMC0024. The structural trend is subparallel to the

fracture orientation of N55oE - N60oE determined for the Frontier formation in the

Apache State #1-36 well (Figure A.3). There appears to be a change in dip, or a

flattening of the structure, just south of line RMC0022, before the formation beds

ramp up sharply in the flexure to the southwest. This change in dip corresponds

approximately with an area of anomalous shear wave rotation results in the fracture

orientation.


Apache Corp. State

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Czar Resources Czar-West

Czar Resources Czar Bennett

ARCO O&G Morton Ranch


Davis Oil Sears-Federal

Davis Oil La Prele St.

Energetics Inc. State

TEXACO Inc. SIMMS

TEXACO Inc. Govt.-Hawks-A

Energetics Inc. --

Apache Corp. Githens

IMPEL Corp. Wallis

EXXON Corp. Box Creek

Chinook Resources Lois

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Apache Corp. Spence

-6000

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Vastar Resources Red Mountain 1-H

Top Niobrara

GR

I-1

GRI-4

GRI-3D

Figure A.2: Structure contour map on top of the Niobrara Formation in the study area, based primarily

on well log tops, with some seismic control (especially in steeply dipping areas). Contour interval

is 100 feet. The figure is taken from Waters, Chen, and Mavko (1994).


Apache Corp. State

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Czar Resources Czar-West

Czar Resources Czar Bennett

ARCO O&G Morton Ranch


Davis Oil Sears-Federal

Davis Oil La Prele St.

Energetics Inc. State

TEXACO Inc. SIMMS

TEXACO Inc. Govt.-Hawks-A

Energetics Inc. --

Apache Corp. Githens

IMPEL Corp. Wallis

EXXON Corp. Box Creek

Chinook Resources Lois

Chinook Resources Tina

Energetics Inc. Sims

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Apache Corp. Spence

Vastar Resources Red Mountain 1-H

Top Frontier

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Figure A.3: Structure contour map on top of the first Frontier Sandstone in the study area, based

primarily on well log tops, with some seismic control (especially in steeply dipping areas).

Contour interval is 100 feet in less steep areas, 500 feet near flexure. The figure is taken from

Waters, Chen, and Mavko (1994).

A.1.2. Regional Stratigraphy and Depositional Environments

Figure A.4 shows the stratigraphic nomentclature developed for various basins in

Wyoming from the Precambrian to the Tertiary. This study is primarily concerned

with the Upper Cretaceous sediments in the southwestern portion of the Powder River

Basin. Below is a summary of the Upper Cretaceous stratigraphy taken from

publications by Barlow and Haun (1966), Hando (1976), Merewether et al (1976),

Prescott (1975), and the Wyoming Geological Association Guidebook (1976).


Parkman Sandstone: offshore marine bar (shelf) sand, deposited in 100-200 feet

water depths; composed of discrete sand lenses encased in siltstone and shale.

Hydrocarbon productive in other areas of the Powder River basin.

Steele Shale: marine shale.

Sussex Sandstone: shelf sand, deposited in 100-200 feet water depths, influenced

by longshore currents; composed of discrete, lenticular sand bodies encased in

interbedded siltstone and shale. Hydrocarbon productive in other areas of the

Powder River basin.

Niobrara Formation: unconformably overlies the Frontier; a series of fractured,

marine chalks and limestones interbedded with calcareous shales and

bentonites. Oil and gas reservoir that is its own source rock. Open fractures

necessary for production due to low porosity and permeability.

First Frontier Sand: uppermost of three sands within the Frontier Formation;

fractured, offshore marine bar sand containing interbedded shales in 3-4

transgressive-regressive cycles; grades upward regionally from marine shale

to sandstone at the top. Reservoirs are thin, low permeability; pay section is

coarse grained, reworked. Lower limit of 8% porosity is necessary for

effective pay thickness.

Mowry Shale: dark grey to black, hard, siliceous shales interbedded with thin

siltstone and sands, plus regionally extensive bentonite beds. Deposited in

very stable depositional environment, greater than 500 feet water depths.


Figure A.4: Stratigraphic nomenclature (Wyoming Geol. Assoc. Guidebook, 1976).


A.1.3. Overpressure

Overpressuring is another potentially important parameter in defining the

characteristics of reservoirs in the southern Powder River basin. The major source

rocks in the southern Powder River basin are Lower Cretaceous shales (Skull Creek

and Mowry) and the Upper Cretaceous Niobrara Formation, which is also a reservoir.

Overpressuring is responsible for preservation of primary porosity at depth and

maintenance of open fractures (Mitchell and Rogers, 1993). This fracture porosity is

important at Silo Field, located more than 100 miles south of the study area, since the

Niobrara in this field is a chalk that tends to have very low permeability. Mitchell

and Rogers (1993) explain the abundance of hydrocarbon shows from

"unconventional" reservoirs in the Upper Cretaceous Frontier equivalents (and the

Niobrara) as being due to preserved primary porosity and the presence of open

fractures.

In the southern Powder River Basin, overpressuring occurs from the Lower

Cretaceous Fall River Formation to the top of the Niobrara, and is caused by

generation and expulsion of hydrocarbons from Lower Cretaceous Mowry and Upper

Cretaceous Niobrara source rocks (Mitchell and Rogers, 1993). Within the Fort

Fetterman site, pressure gradients from drillstem tests range from 0.47 psi/ft in the

southeast corner of T33N R71W to 0.51 psi/ft to the northwest (Mitchell and Rogers,

1993), with an overall increase in pressure gradient from south to north.

A.2 Fracture Existence and Attributes

Core, outcrop, LandSat, magnetic, and resistivity image data (FMS log) of natural

fractures can help guide the seismic interpretation of fractured reservoirs. I review

the published direct observations of fractures in south Powder River Basin, east-

central Wyoming (May et al., 1996), and at Moxa Arch and adjacent Green River

Basin, southwestern Wyoming (Laubach, 1991, 1992a, 1992b; Dutton et al., 1992).


A.2.1. Fractures at Fort Fetterman Site and South Powder River Basin

May et al. (1996) analyzed the LandSat, magnetic and outcrop data in the south

Powder River Basin. I summarized their observations below:

1. N70E set: A regional fracture set (N70E) is well represented in Cretaceous units

throughout the southern Casper Arch and northern Laramie Range, and is not

observed in Tertiary strata. In the outcrop, these fractures are planar, parallel,

and perpendicular to bedding. Fractures spacing ranges from 10 cm to 2 cm. The

N70E-trending fractures are rarely mineralized. When they are calcite-filled, the

fracture porosity for the calcite is likely due to enhanced opening during

Laramide folding.

2. N110E set: A younger N110E-trending fracture set is observed in Tertiary strata,

and locally in Cretaceous strata. On the basis of the fracture truncation

relationships, the N70E-trending regional fracture set predates many other

fractures. The younger fracture trends are commonly calcite-filled.

3. Stress direction: The N70E-trending fractures are now interpreted as dilational

extension fractures orientated parallel to an inferred east-northeast-orientated

maximum horizontal stress associated with the late Cretaceous thrust belt. This

set is thought to have been subsequently rotated and overprinted by the Laramide

folds and uplifts of the region.

4. Fractures terminate at bedding boundary: All fractures, regardless of

orientation, are better developed in thinner-bedded, well-cemented lithologies and

commonly terminate at thin shale or bentonite beds. Massive, poorly-cemented

beds display fewer fractures.

A.2.2. Fractures in the Moxa Arch region and the Green River Basin

Laubach (1991, 1992a, 1992b) and Dutton et al. (1992) studied fracture patterns

in the Frontier Formation by examining the cores and outcrops in the Moxa Arch


region and adjacent areas of the Green River Basin in southwestern Wyoming. I

include a summary of their observations and analysis below as a supplementary

reference. Knowledge of the in situ fracture patterns can help earth scientists to

justify the geological rationality of the fracture models used in the seismic fracture

characterization.

1. Occurrence: Natural fractures, occuring in a depth range 7195 to 16130 ft, are

sparse but persistent features of Frontier Formation core. They include vertical to

sub-vertical extension fractures and small faults.

2. Orientation: Core observation shows that in the Frontier Formation, two sets of

fractures locally occur in the subsurface. One set of fractures has eastern or

northeastern strikes, and another has northern strikes. The two fracture sets rarely

occur in the same sandstone bed.

3. Material in fractures: The north-striking fractures formed early. They are

confined to only a few beds, and generally tightly filled with calcite. East-striking

fractures in the Frontier outcrop west of Fontenelle, Wyoming are filled or partly

filled with calcite, and locally, subsidiary quartz and clay minerals. Only a few

show petrographic evidence, such as euhedral crystals lining fractures, which

indicate that fractures were persistently open in the subsurface.

4. Spacing: East-striking fractures in the Frontier outcrop are arranged in swarms.

Swarm width ranges from 2 inches (5 cm) to more than 160 ft (50 m). Fracture

spacing within swarms ranges from less than 1 inch (2.5 cm) to 15 ft (5 m).

5. Dimension: In the Frontier outcrop, fracture length ranges from centimeters to

125 ft (38 m). For fractures more than 3 ft (1 m) long, mean fracture length is 23

ft (7 m). Fractures tend to end vertically within sandstone beds, or at bed

boundaries, and rarely cross the shales between sandstone beds. Heights of

fractures are similar to or less than the bed thickness, ranging from less than an

inch to several tens of feet. Length-to-height ratios can be greater than 10:1.

6. Fracture shape and aperture: The dominant, bed-normal fractures typically

have simple lens- to parallel-sided shapes. Mineralized extension fractures in


Frontier Formation core are typically narrow, are commonly < 0.01 inch wide.

Wide fractures are filled or partly filled with minor quartz and calcite. Height-to-

width ratios of 500 to 1,500 are typical.

7. Connectivity: Where a single fracture set is present, connectivity is generally less

than 50 percent; and where two or more fracture sets are present, connectivity can

approach 100 percent.

A.3 References

Barlow, J. A., and Haun, J. D., 1966, Regional stratigraphy of Frontier Formation and

relation to Salt Creek field, Wyoming: AAPG Bulletin, 50, 2185-2196.

Dickinson, W. R., Klute, M. A., Hayes, M. J., Janecke, S. U., Lundin, E. R.,

McKittrick, M. A., and Olivares, M. D., 1988, Paleogeographic and paleotectonic

setting of Laramide sedimentary basins in the central Rocky Mountain region:

GSA Bulletin, 100, 1023-1039.

Dutton, S.P., Hamlin, H. S., and Laubach, S. E., 1992, Geologic controls on reservoir

properties of low-permeability sandstone, Frontier Formation, Moxa Arch,

southwest Wyoming: The University of Texas at Austin, Bureau of Economic

Geology, topical report no. GRI-92/0127, prepared for the Gas Research Institute,

199 p.

Hando, R. E., 1976, Powell-Ross field, Converse County, Wyoming: Wyoming

Geological Association Guidebook, 28th Annual Field Conference, 139-145.

Laubach, S.E., 1991, Fracture patterns in low-permeability-sandstone gas reservoir

rocks in the Rocky Mountain region, SPE Paper 231853, Proceedings, Joint SPE

Rocky Mountain regional meeting/low-permeability reservoir symposium, 501-

510

Laubach, S.E., 1992a, Identifying key reservoir elements in low-permeability

sandstones: natural fractures in the Frontier Formation, southwestern Wyoming,

In Focus-Tight Gas Sands, GRI, Chicago, IL, 8, No. 2, 3-11.


Laubach, S.E., 1992b, Fracture networks in selected Cretaceous sandstones of the

Green River and San Juan basins, Wyoming, New Mexico, and Colorado,

Geological Studies Relevant to Horizontal Drilling in Western North America, ed.

Schmoker, J.W., Coalson, E.B., Brown, C.A., 115-127



basement fractures, ARCO-GRI fractured reservoir project report

Merewether, E. A., Cobban, W. A., and Spencer, C. W., 1976, The Upper Cretaceous

Frontier Formation in the Kaycee-Tisdale Mountain area, Johnson County,

Wyoming, Wyoming Geological Association Guidebook, 28th Annual Field

Conference, 33-44.

Mitchell, G. C., and Rogers, M. H., 1993, Extensional tectonic influence on Lower

and Upper Cretaceous stratigraphy and reservoirs, southern Powder River basin,

Wyoming: The Mountain Geologist, 30, no. 2, 54-68.

Prescott, M. W., 1975, Spearhead Ranch field, Converse County, Wyoming: Rocky

Mountain Association of Geologists, A symposium on deep drilling frontiers in

the central Rocky Mountains, 239-244.

Walters, R., Chen, W., Mavko, G., 1994, Regional geological framework and site

description.

Wyoming Geological Association, 1976, Guidebook, 28th Annual Field Conference,

Geology and energy resources of the Powder River: Casper, Wyoming, 328 p.

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